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@BOOK{sontag_sysbionotes,
PUBLISHER = {Online only.},
TITLE = {Notes on Mathematical Systems Biology (online)},
YEAR = {2026},
AUTHOR = {E.D. Sontag},
ALTEDITOR = {},
OPTADDRESS = {},
OPTEDITION = {},
OPTMONTH = {},
NOTE = {Continuously updated. If the link does not work, then copy/paste this: http://drive.google.com/drive/folders/1lIRqaCPeXMVZGoY-44bBsvtnsHtlRfIO?usp=sharing},
OPTNUMBER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, mathematical biology},
PDF = {https://drive.google.com/drive/folders/1lIRqaCPeXMVZGoY-44bBsvtnsHtlRfIO?usp=drive_link}
}
@ARTICLE{MAli_angeli_sontag_contractions_learn,
AUTHOR = {M.A. Al-Radhawi and D. Angeli and E.D. Sontag},
JOURNAL = {SIAM J Applied Dynamical Systems},
TITLE = {On structural contraction of biological interaction
networks},
YEAR = {2026},
OPTMONTH = {},
NOTE = {To appear. Preprint in: arXiv, 2025: http://arxiv.org/abs/2307.13678.},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, matrix measures,
logarithmic norms},
ABSTRACT = {In previous work, we have developed an approach to
understanding the long-term dynamics of classes of chemical reaction
networks, based on rate-dependent Lyapunov functions. In this paper,
we show that stronger notions of convergence can be established by
proving contraction with respect to non-standard norms. This enables
us to show that such networks entrain to periodic inputs. We
illustrate our theory with examples from signaling pathways and
genetic circuits.}
}
@ARTICLE{2025_chen_mali_levine_sontag_notch,
AUTHOR = {T. Chen and M. A. Al-Radhawi and H. Levine and
E. D. Sontag},
JOURNAL = {Physical Biology},
TITLE = {The interaction between dynamic ligand signaling and
epigenetics in Notch-induced cancer metastasis},
YEAR = {2026},
OPTMONTH = {},
NOTE = {Also 2025 biorxiv 10.1101/2025.05.19.654987},
OPTNUMBER = {},
PAGES = {016002},
VOLUME = {23},
KEYWORDS = {metastasis, melanoma, Notch signaling, miR-222,
epigenetics, drug resistance, therapy resistance},
URL = {http://iopscience.iop.org/article/10.1088/1478-3975/ae2c34},
PDF = {../../FTPDIR/2026_chen_notch_delta_physbio_reprint_and_si.pdf},
ABSTRACT = {Metastatic melanoma presents a formidable challenge in
oncology due to its high invasiveness and resistance to current
treatments. Central to its ability to metastasize is the Notch
signaling pathway, which, when activated through direct cell-cell
interactions, propels cells into a metastatic state through
mechanisms akin to the epithelial-mesenchymal transition (EMT). While
the upregulation of miR-222 has been identified as a critical step in
this metastatic progression, the mechanism through which this
upregulation persists in the absence of active Notch signaling
remains unclear. Here we introduce a dynamical system model that
integrates miR-222 gene regulation with histone feedback mechanisms.
Through computational analysis, we delineate the non-linear decision
boundaries that govern melanoma cell fate transitions, taking into
account the dynamics of Notch signaling and the role of epigenetic
modifications. Our approach highlights the critical interplay between
Notch signaling pathways and epigenetic regulation in dictating the
fate of melanoma cells.},
DOI = {10.1088/1478-3975/ae2c34}
}
@ARTICLE{2025_pinns,
AUTHOR = {A. Darabi and Z. An and M.A. Al-Radhawi and W. Cho and
M. Siami and E.D. Sontag},
JOURNAL = {Mathematical Biosciences},
TITLE = {Combining model-based and data-driven models: an
application to synthetic biology resource competition},
YEAR = {2026},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {109649},
VOLUME = {396},
KEYWORDS = {mechanistic models, machine learning, neural networks,
resource competition, synthetic biology},
URL = {https://doi.org/10.1101/2025.03.09.642275},
PDF = {../../FTPDIR/2026_epinns_reprint.pdf},
ABSTRACT = {This work explores the integration of machine learning
(ML) and mechanistic models (MM). While ML has demonstrated
remarkable success in data-driven modeling across engineering,
biology, and other scientific fields, MM remain essential for their
interpretability and capacity to extrapolate beyond observed
conditions based on established principles such as chemical kinetics
and physiological processes. However, MM can be labor-intensive to
construct and often rely on simplifying assumptions that may not
fully capture real-world complexity. It is thus desirable to combine
MM and ML approaches so as to enable more robust predictions,
enhanced system insights, and improved handling of sparse or noisy
data. A key challenge when doing so is ensuring that ML components do
not disregard mechanistic information, potentially leading to
overfitting or reduced interpretability. To address that challenge,
this paper introduces the idea of Partially Uncertain Model
Structures (PUMS) and investigates conditions that discourage the ML
components from ignoring mechanistic constraints. This work also
introduces the concept of embedded Physics-Informed Neural Networks
(ePINNs), which consist of two loss-sharing neural networks that
seamlessly blend ML and MM components. This work arose in the study
of the context problem in synthetic biology. Engineered genetic
circuits may exhibit unexpected behavior in living cells due to
resource sharing. To illustrate the advantages of the ePINNs
approach, this paper applies the framework to a gene network model
subject to resource competition, demonstrating the effectiveness of
this hybrid modeling approach in capturing complex system
interactions while maintaining physical consistency.}
}
@ARTICLE{2025_toxicity,
AUTHOR = {J.L. Gevertz and H.V. Jain and I. Kareva and K.P. Wilkie and
J. Brown and Y.P. Huang and E.D. Sontag and V. Vinogradov and
M. Davies},
JOURNAL = {npj Systems Biology and Applications},
TITLE = {Delaying cancer progression by integrating toxicity
constraints in a model of adaptive therapy},
YEAR = {2026},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {11},
VOLUME = {12},
KEYWORDS = {toxicity, adaptive anti-cancer therapy,
virtual populations, therapy resistance, drug resistance,
mathematical model, mathematical oncology},
PDF = {../../FTPDIR/gevertz_et_al_toxicity_npj_2026.pdf},
ABSTRACT = {Cancer therapies often fail when intolerable toxicity or
drug-resistant cancer cells undermine otherwise effective treatment
strategies. Over the past decade, adaptive therapy has emerged as a
promising approach to postpone emergence of resistance by altering
dose timing based on tumor burden thresholds. Despite encouraging
results, these protocols often overlook the crucial role of
toxicity-induced treatment breaks, which may permit tumor regrowth.
Herein, we explore the following question: would toxicity feedback
improve or hinder the efficacy of adaptive therapy? To address this
question, we propose a mathematical framework for incorporating toxic
feedback into treatment design. We find that the degree of
competition between sensitive and resistant populations, along with
the growth rate of resistant cells, critically modulates the impact
of toxicity feedback on time to progression. Further, our model
identifies circumstances where strategic treatment breaks, which may
be based on either tumor size or toxicity, can mitigate overtreatment
and extend time to progression, both at the baseline parameterization
and across a heterogeneous virtual population. Taken together, these
findings highlight the importance of integrating toxicity
considerations into the design of adaptive therapy.}
}
@ARTICLE{2025_11_oliveira_jatkar_sontag_general_loss_overparametrized,
AUTHOR = {de Oliveira, A.C.B and D.D. Jatkar and E.D. Sontag},
JOURNAL = {Proceedings of the 8th Annual Learning for Dynamics & Control Conference (L4DC)},
TITLE = {On the convergence of overparameterized problems:
Inherent properties of the compositional structure of neural networks},
YEAR = {2026},
OPTMONTH = {},
NOTE = {To appear. Also 2025 arXiv:2511.09810 [cs.LG]},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, neural networks, optimization, overparameterization},
ABSTRACT = {This paper investigates how the compositional structure
of neural networks shapes their optimization landscape and training
dynamics. We analyze the gradient flow associated with
overparameterized optimization problems, which can be interpreted as
training a neural network with linear activations. Remarkably, we
show that the global convergence properties can be derived for any
cost function that is proper and real analytic. We then specialize
the analysis to scalar-valued cost functions, where the geometry of
the landscape can be fully characterized. In this setting, we
demonstrate that key structural features -- such as the location and
stability of saddle points -- are universal across all admissible
costs, depending solely on the overparameterized representation
rather than on problem-specific details. Moreover, we show that
convergence can be arbitrarily accelerated depending on the
initialization, as measured by an imbalance metric introduced in this
work. Finally, we discuss how these insights may generalize to neural
networks with sigmoidal activations, showing through a simple example
which geometric and dynamical properties persist beyond the linear
case.},
DOI = {https://doi.org/10.48550/arXiv.2511.09810}
}
@INPROCEEDINGS{2026acc_stochastic,
AUTHOR = {L. Cui and Z.P. Jiang and E. D. Sontag},
BOOKTITLE = {2026 American Control Conference (ACC)},
TITLE = {Small-covariance noise-to-state stability of stochastic
systems and its applications to stochastic gradient dynamics},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {To appear. Also 2025 arXiv:2509.24277},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, noise to state stability, input to state stability,
dynamics of algorithms, stochastic systems},
PDF = {../../FTPDIR/2025_arxiv_cui_jiang_sontag_nss_gradients.pdf},
ABSTRACT = {This paper studies gradient dynamics subject to additive
stochastic noise, which may arise from sources such as stochastic
gradient estimation, measurement noise, or stochastic sampling
errors. To analyze the robustness of such stochastic gradient
systems, the concept of small-covariance noise-to-state stability
(NSS) is introduced, along with a Lyapunov-based characterization.
Furthermore, the classical Polyak–Lojasiewicz (PL) condition on the
objective function is generalized to the $\mathcal{K}$-PL condition
via comparison functions, thereby extending its applicability to a
broader class of optimization problems. It is shown that the
stochastic gradient dynamics exhibit small-covariance NSS if the
objective function satisfies the $\mathcal{K}$-PL condition and
possesses a globally Lipschitz continuous gradient. This result
implies that the trajectories of stochastic gradient dynamics
converge to a neighborhood of the optimum with high probability, with
the size of the neighborhood determined by the noise covariance.
Moreover, if the $\mathcal{K}$-PL condition is strengthened to a
$\mathcal{K}_\infty$-PL condition, the dynamics are NSS; whereas if
it is weakened to a general positive-definite-PL condition, the
dynamics exhibit integral NSS. The results further extend to
objectives without globally Lipschitz gradients through appropriate
step-size tuning. The proposed framework is further applied to the
robustness analysis of policy optimization for the linear quadratic
regulator (LQR) and logistic regression.},
DOI = {https://doi.org/10.48550/arXiv.2509.24277}
}
@INPROCEEDINGS{2026cdc_oliveira,
AUTHOR = {A. Oliveira and de Oliveira, A. C. B. and M. Sznaier and
E. D. Sontag},
BOOKTITLE = {Proc. 65th IEEE Conference on Decision and Control (CDC)},
TITLE = {On incremental and semi-global exponential stability of
gradient flows satisfying generalized Lojasiewicz inequalities},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Submitted. Also arXiv arXiv:2603.25822},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, contractions, contractive systems},
ABSTRACT = {The Lojasiewicz inequality characterizes objective-value
convergence along gradient flows and, in special cases, yields
exponential decay of the cost. However, such results do not directly
imply convergence of the state. In this paper, we use contraction
theory to derive state-space guarantees for gradient systems
satisfying generalized Lojasiewicz inequalities. We first show that,
when the objective has a unique strongly convex minimizer, the
generalized Lojasiewicz inequality implies semi-global exponential
stability; on arbitrary compact subsets, this yields exponential
stability. We then give two curvature-based sufficient conditions,
together with constraints on the Lojasiewicz rate, under which the
nonconvex gradient flow is globally incrementally exponentially
stable, a property strictly stronger than global exponential
stability. A few examples are presented at the end of the paper to
validate the proposed theory.}
}
@INPROCEEDINGS{25moh_arthur_eduardo_acc_submission,
AUTHOR = {M.K. Wafi and de Oliveira, A.C.B and E.D. Sontag},
BOOKTITLE = {2026 American Control Conference (ACC)},
TITLE = {On the (almost) global exponential convergence of
overparameterized policy optimization for the LQR problem},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {To appear. See also 2025 arXiv:2510.02140},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, machine learning, artificial intelligence,
dynamics of algorithms, LQR, reinforcement learning},
PDF = {../../FTPDIR/2025_arxiv_wafi_deoliveira_sontag_overparametrized_lqr_global_exponential.pdf},
ABSTRACT = {In this work we study the convergence of gradient
methods for nonconvex optimization problems -- specifically the
effect of the problem formulation to the convergence behavior of the
solution of a gradient flow. We show through a simple example that,
surprisingly, the gradient flow solution can be exponentially or
asymptotically convergent, depending on how the problem is
formulated. We then deepen the analysis and show that a policy
optimization strategy for the continuous-time linear quadratic
regulator (LQR) (which is known to present only asymptotic
convergence globally) presents almost global exponential convergence
if the problem is overparameterized through a linear feed-forward
neural network (LFFNN). We prove this qualitative improvement always
happens for a simplified version of the LQR problem and derive
explicit convergence rates for the gradient flow. Finally, we show
that both the qualitative improvement and the quantitative rate gains
persist in the general LQR through numerical simulations.}
}
@INPROCEEDINGS{26cdc_moh_arthur_eduardo_cdr,
AUTHOR = {M.K. Wafi and de Oliveira, A.C.B and E.D. Sontag},
BOOKTITLE = {Proc. 65th IEEE Conference on Decision and Control (CDC)},
TITLE = {When is cumulative dose response monotonic? Analysis of
incoherent feedforward motifs},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Submitted. Also arXiv:2604.01573},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {dose response, perfect adaptation, systems biology,
incoherent feedforward loops, transient behavior},
ABSTRACT = {We study the monotonicity of the cumulative dose
response (cDR) for a class of incoherent feedforward motif (IFFMs)
systems with linear intermediate dynamics and nonlinear output
dynamics. While the instantaneous dose response (DR) may be
nonmonotone with respect to the input, the cDR can still be monotone.
To analyze this phenomenon, we derive an integral representation of
the sensitivity of cDR with respect to the input and establish
general sufficient conditions for both monotonicity and
non-monotonicity. These results reduce the problem to verifying
qualitative sign properties along system trajectories. We apply this
framework to four canonical IFFM systems and obtain a complete
characterization of their behavior. In particular, IFFM1 and IFFM3
exhibit monotone cDR despite potentially non-monotone DR, while IFFM2
is monotone already at the level of DR, which implies monotonicity of
cDR. In contrast, IFFM4 violates these conditions, leading to a loss
of monotonicity. Numerical simulations indicate that these properties
persist beyond the structured initial conditions used in the
analysis. Overall, our results provide a unified framework for
understanding how network structure governs monotonicity in
cumulative input–output responses.}
}
@INPROCEEDINGS{2026acc_wang_sontag_delvecchio,
AUTHOR = {J. Wang and E.D. Sontag and D. Del Vecchio},
BOOKTITLE = {2026 American Control Conference (ACC)},
TITLE = {Modular machine learning with applications to genetic
circuit composition},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {To appear. Also 2025 Preprint in arXiv 2509.19601},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {biomolecular systems, machine learning,
nonlinear systems identification},
PDF = {../../FTPDIR/2025_modular_wang_sontag_delvecchio.pdf},
ABSTRACT = {In several applications, including synthetic biology,
one often has input/output data on a system composed of many modules,
and although the modules’ input/output functions and signals may be
unknown, knowledge of the composition architecture can significantly
reduce the amount of training data required to learn the system’s
input/output mapping. Learning the modules’ input/output functions
is also necessary for designing new systems from different
composition architectures. Here, we propose a modular learning
framework that incorporates prior knowledge of the system’s
compositional structure to (a) identify the composing modules’
input/output functions from the system’s input/output data and (b)
achieve this using a reduced amount of data compared to what would be
required without knowledge of the compositional structure. To achieve
this, we introduce the notion of modular identifiability, which
allows recovery of modules’ input/output functions from a subset of
the system’s input/output data, and we provide theoretical
guarantees on a class of systems motivated by genetic circuits. We
demonstrate the theory in computational studies showing that a neural
network (NNET) that accounts for the compositional structure can
learn the composing modules’ input/output functions and predict the
system’s output on inputs outside of the training set distribution.
By reducing the need for experimental data and enabling modules’
identification, this framework offers the potential to ease the
design of synthetic biological circuits and of multi-module systems
more generally.}
}
@INPROCEEDINGS{2026cdc_lipshitz,
AUTHOR = {de Oliveira, A. C. B. and R. Wang and I.R. Manchester and
E. D. Sontag},
BOOKTITLE = {Proc. 65th IEEE Conference on Decision and Control (CDC)},
TITLE = {Remarks on Lipschitz-minimal interpolation:
Generalization bounds and neural network implementation},
YEAR = {2026},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Submitted. Also arXiv:2603.19524},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
ABSTRACT = {This note establishes a theoretical framework for
finding (potentially overparameterized) approximations of a function
on a compact set with a-priori bounds for the generalization error.
The approximation method considered is to choose, among all functions
that (approximately) interpolate a given data set, one with a minimal
Lipschitz constant. The paper establishes rigorous generalization
bounds over practically relevant classes of approximators, including
deep neural networks. It also presents a neural network
implementation based on Lipschitz-bounded network layers and an
augmented Lagrangian method. The results are illustrated for a
problem of learning the dynamics of an input-to-state stable system
with certified bounds on simulation error.}
}
@INCOLLECTION{2024_robotics,
AUTHOR = {de Oliveira, A.C.B. and M. Siami and E. D. Sontag},
BOOKTITLE = {Geometry, Topology and Control System Design: Proceedings of a Banff International Research Station Workshop},
PUBLISHER = {American Institute of Mathematical Sciences Press},
TITLE = {Regularising numerical extremals along singular arcs: a
Lie-theoretic approach},
YEAR = {2025},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {M.A. Belabbas},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {75-89},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {optimal control, nonlinear control, Lie algebras,
robotics},
PDF = {../../FTPDIR/oliveira_siami_sontag_regularising_extremals_reprint.pdf},
ABSTRACT = {Numerical ``direct'' approaches to time-optimal control
often fail to find solutions that are singular in the sense of the
Pontryagin Maximum Principle. These approaches behave better when
searching for saturated (bang-bang) solutions. In previous work by
one of the authors, singular solutions were theoretically shown to
exist for the time-optimal problem for two-link manipulators under
hard torque constraints. The theoretical results gave explicit
formulas, based on Lie theory, for singular segments of trajectories,
but the global structure of solutions remains unknown. In this work,
we show how to effectively combine these theoretically found formulas
with the use of general-purpose optimal control softwares. By using
the explicit formula given by theory in the intervals where the
numerical solution enters a singular arcs, we not only obtain an
algebraic expression for the control in that interval, but we are
also able to remove artifacts present in the numerical solution. In
this way, the best features of numerical algorithms and theory
complement each other and provide a better picture of the global
optimal structure. We showcase the technique on a 2 degrees of
freedom robotic arm example, and also propose a way of extending the
analyzed method to robotic arms with higher degrees of freedom
through partial feedback linearization, assuming the desired task can
be mostly performed by a few of the degrees of freedom of the robot
and imposing some prespecified trajectory on the remaining joints.}
}
@ARTICLE{2025ejc_biswas_sontag_cowan,
AUTHOR = {D. Biswas and E.D Sontag and N.J. Cowan},
JOURNAL = {European Journal of Control},
TITLE = {An exact active sensing strategy for a class of
bio-inspired systems},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Also in Proc. 23rd European Control Conference, and longer version in https://arxiv.org/abs/2411.06612.},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {active sensing, systems biology, observability,
nonlinear control, nonlinear systems, active sensing,
weakly electric fish, observability, biological systems,
nonlinear system theory, linear time-varying systems},
URL = {https://doi.org/10.1016/j.ejcon.2025.101361},
PDF = {../../FTPDIR/2025_biswas_sontag_cowan_active_sensing_ejc.pdf},
ABSTRACT = {We consider a general class of translation-invariant
systems with a specific category of output nonlinearities motivated
by biological sensing. We show that no dynamic output feedback can
stabilize this class of systems to an isolated equilibrium point. To
overcome this fundamental limitation, we propose a simple control
scheme that includes a low-amplitude periodic forcing function akin
to so-called "active sensing" in biology, together with nonlinear
output feedback. Our analysis shows that this approach leads to the
emergence of an exponentially stable limit cycle. These findings
offer a provably stable active sensing strategy and may thus help to
rationalize the active sensing movements made by animals as they
perform certain motor behaviors.}
}
@ARTICLE{2025_arxiv_cui_jiang_sontag_braaz_discrete_time_iss_gradient,
AUTHOR = {L. Cui and Z.P. Jiang and E.D. Sontag and R.D. Braatz},
JOURNAL = {Automatica},
TITLE = {Perturbed gradient descent algorithms are
small-disturbance input-to-state stable},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Submitted. Also arXiv:2507.02131},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, input-to-state stability, dynamics of algorithms,
policy optimization, linear quadratic regulator},
PDF = {../../FTPDIR/2025_arxiv_cui_jiang_sontag_braaz_discrete_time_iss_gradient.pdf},
ABSTRACT = {This article investigates the robustness of gradient
descent algorithms under perturbations. The concept of
small-disturbance input-to-state stability (ISS) for discrete-time
nonlinear dynamical systems is introduced, along with its Lyapunov
characterization. The conventional linear Polyak-Lojasiewicz (PL)
condition is then extended to a nonlinear version, and it is shown
that the gradient descent algorithm is small-disturbance ISS provided
the objective function satisfies the generalized nonlinear PL
condition. This small-disturbance ISS property guarantees that the
gradient descent algorithm converges to a small neighborhood of the
optimum under sufficiently small perturbations. As a direct
application of the developed framework, we demonstrate that the LQR
cost satisfies the generalized nonlinear PL condition, thereby
establishing that the policy gradient algorithm for LQR is
small-disturbance ISS. Additionally, other popular policy gradient
algorithms, including natural policy gradient and Gauss-Newton
method, are also proven to be small-disturbance ISS.},
DOI = {https://doi.org/10.48550/arXiv.2507.02131}
}
@ARTICLE{duvall_sontag_siads,
AUTHOR = {A. Duvall and M. Ali Al-Radhawi and D. Jatkar and
E. D. Sontag},
JOURNAL = {},
TITLE = {Interplay between contractivity and monotonicity for
reaction networks},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {reaction networks, monotone systems, reaction networks,
reaction networks, contractions, contractive systems},
URL = {https://arxiv.org/abs/2404.18734},
ABSTRACT = {We establish a new relationship between monotonicity and
contractivity and use this connection to describe a new general class
of weakly contractive reaction networks. The new class is
characterized by the stoichiometry matrix of the reaction network
admitting a precise matrix factorization that can be verified
computationally. Reaction networks in this class are weakly
contractive, implying global convergence to equilibria under
appropriate technical conditions. Furthermore, we describe the novel
subclass of cross-polytope networks. We also show that our results
provide a unified proof of global convergence for several classes of
networks previously studied in the literature. The practical
relevance of the results is demonstrated by examples from systems
biology and signaling pathways.}
}
@ARTICLE{2024_gevertz_greene_prosperi_comandantelou_sontag_therapeutic_tolerance,
AUTHOR = {J.L Gevertz and J.M Greene and S. Prosperi and
N. Comandante-Lou and E.D. Sontag},
JOURNAL = {npj Systems Biology and Applications},
TITLE = {Understanding therapeutic tolerance through a
mathematical model of drug-induced resistance},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-15},
VOLUME = {11},
KEYWORDS = {cancer, drug resistance, therapy resistance,
phenotypic plasticity, mathematical models, optimal control},
PDF = {../../FTPDIR/2025_03_gevertz_greene_prosperi_comandantelou_sontag_therapeutic_tolerance_published.pdf},
ABSTRACT = {There is growing recognition that phenotypic plasticity
enables cancer cells to adapt to various environmental conditions. An
example of this adaptability is the persistence of an initially
sensitive population of cancer cells in the presence of therapeutic
agents. Understanding the implications of this drug-induced
resistance is essential for predicting transient and long-term tumor
tumor dynamics subject to treatment. This paper introduces a
mathematical model of this phenomenon of drug-induced resistance
which provides excellent fits to time-resolved in vitro experimental
data. From observational data of total numbers of cells, the model
unravels the relative proportions of sensitive and resistance
subpopulations, and quantifies their dynamics as a function of drug
dose. The predictions are then validated using data on drug doses
which were not used when fitting parameters. The model is then used,
in conjunction with optimal control techniques, in order to discover
dosing strategies that might lead to better outcomes as quantified by
lower total cell volume.}
}
@ARTICLE{gupta_sontag_cdr,
AUTHOR = {A. Gupta and E. D. Sontag},
JOURNAL = {Royal Society Interface},
TITLE = {Cumulative dose responses for adapting biological
systems},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {20240877},
VOLUME = {22},
KEYWORDS = {dose response, perfect adaptation, systems biology,
incoherent feedforward loops, integral feedback, immunology, T cells},
PDF = {../../FTPDIR/2025_gupta_sontag_cdr_rsi_reprint.pdf},
ABSTRACT = {This paper introduces the notion of cumulative dose
response (cDR). The cDR is the area under the plot of a response
variable, an integral taken over a fixed time interval and seen as a
function of an input parameter. This work was motivated by the
accumulation of cytokines resulting from T cell stimulation, where a
non-monotonic cDR has been observed experimentally. However, the
notion is of general applicability. A surprising conclusion is that
incoherent feedforward loops studied in the systems biology
literature, though capable of non-monotonic dose responses, can be
mathematically shown to always result in monotonic cDR.}
}
@ARTICLE{2025_11_dcas9_competition,
AUTHOR = {D.D. Jatkar and M.A. Al-Radhawi and C. A. Voigt and
E.D. Sontag},
JOURNAL = {bioRxiv},
TITLE = {Modeling and minimization of dCas9-induced competition
in CRISPRi-based genetic circuits},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2025.11.05.686856},
OPTVOLUME = {},
KEYWORDS = {CRISPRi, retroactivity, feedback, logic-circuit,
synthetic biology},
PUBLISHER = {Cold Spring Harbor Laboratory},
URL = {https://www.biorxiv.org/content/early/2025/11/05/2025.11.05.686856},
ABSTRACT = {Implementing logic functions in living cells is a
fundamental area of interest among synthetic biologists. The goal of
designing biochemical circuits in synthetic biology is to make
modular and tractable systems that perform well with predictable
behaviors. Developing formalisms towards the design of such systems
has proven to be difficult with the diverse retroactive effects that
appear with respect to the context of the cell. Repressor-based
circuits have various applications in biosynthesis, therapeutics, and
bioremediation. Particularly using CRISPRi, competition for
components of the system (unbound dCas9) can affect the achievable
dynamic range of repression. Moreover, the toxicity of dCas9 via
non-specific binding inhibits high levels of expression and limits
the performance of genetic circuits. In this work, we study the
computation of Boolean functions through CRISPRi based circuits built
out of NOT and NOR gates. We provide algebraic expressions that allow
us to evaluate the steady-state behaviors of any realized circuit.
Our mathematical analysis reveals that the effective
non-cooperativity of any given gate is a major bottleneck for
increasing the dynamic range of the outputs. Further, we find that
under the condition of competition between promoters for dCas9,
certain circuit architectures perform better than others depending on
factors such as circuit depth, fan-in, and fan-out. We pose
optimization problems to evaluate the effects engineerable parameter
values to find regimes in which a given circuit performs best. This
framework provides a mathematical template and computational library
for evaluating the performance of repressor-based circuits with a
focus on effective cooperativity.},
DOI = {10.1101/2025.11.05.686856}
}
@ARTICLE{2025_activator_repressor_jatkar_et_al,
AUTHOR = {D.D. Jatkar and K. M. Aravind and E. D. Sontag and
Del Vecchio, D.},
JOURNAL = {bioRxiv, being submitted.},
TITLE = {Paradoxical gene regulation explained by competition for
genomic sites},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2025.11.27.691022},
OPTVOLUME = {},
PUBLISHER = {Cold Spring Harbor Laboratory},
URL = {https://www.biorxiv.org/content/early/2025/11/27/2025.11.27.691022},
ABSTRACT = {Understanding how opposing regulatory factors shape gene
expression is essential for interpreting complex biological systems.
A motivating observation, drawn from cancer epigenetics, is that
removing an activating factor can sometimes lead to higher, not
lower, expression of a gene that is also subject to repression. This
counterintuitive behavior suggests that competition between
activators and repressors for limited genomic binding sites may
produce unexpected transcriptional outcomes. Prior theoretical work
proposed this mechanism, but it has been difficult to test directly
in natural systems, where layers of chromatin regulation obscure
causal relationships. This paper introduces a fully synthetic,
tunable genetic platform in a prokaryotic model system that isolates
this competition mechanism in a clean and interpretable setting. The
engineered construct contains a target gene with binding sites for
both an activator and a repressor, together with a separate decoy
region that carries overlapping binding sites for the same
regulators. Activator and repressor functions are implemented using
CRISPRa and CRISPRi, which permit independent control of regulator
expression levels and binding affinities. Using this minimal system,
the paper shows that increasing activator expression can reduce
expression of the target gene when both regulators are present,
consistent with the prediction that additional activator molecules
displace the repressor from decoy sites and allow it to more
effectively repress the target. By demonstrating how competition
alone can invert expected regulatory responses, this synthetic
framework provides a validated model for understanding similar
paradoxical behaviors in natural regulatory networks and establishes
a foundation for future studies in more complex mammalian contexts.},
DOI = {10.1101/2025.11.27.691022}
}
@ARTICLE{kvalheim_sontag_dynamic_autoencoding_arxiv,
AUTHOR = {M. D. Kvalheim and E. D. Sontag},
JOURNAL = {arXiv},
TITLE = {Autoencoding dynamics: Topological limitations and
capabilities},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Journal version submitted.},
OPTNUMBER = {},
PAGES = {2511.04807},
OPTVOLUME = {},
KEYWORDS = {autoencoders, dynamical systems, encoding dynamics,
differential geometry},
URL = {https://arxiv.org/abs/2511.04807},
PDF = {../../FTPDIR/2025_11_kvalheim_sontag_dynamic_autoencoding_arxiv04807v2.pdf},
ABSTRACT = {Given a "data manifold" $M\subset \mathbb{R}^n$ and
"latent space" $\mathbb{R}^\ell$, an autoencoder is a pair of
continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\to
\mathbb{R}^\ell$ and "decoder" $D\colon \mathbb{R}^\ell\to
\mathbb{R}^n$ such that the "round trip" map $D\circ E$ is as close
as possible to the identity map $\mbox{id}_M$ on $M$. We present
various topological limitations and capabilites inherent to the
search for an autoencoder, and describe capabilities for autoencoding
dynamical systems having $M$ as an invariant manifold.}
}
@ARTICLE{kvalheim_sontag_grobman,
AUTHOR = {M. D. Kvalheim and E. D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Global linearization of asymptotically stable systems
without hyperbolicity},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {106163},
VOLUME = {203},
KEYWORDS = {linearization, Hartman-Grobman Theorem},
PDF = {../../FTPDIR/2025_kvalheim_sontag_global_linearization.pdf},
ABSTRACT = {We give a proof of an extension of the Hartman-Grobman
theorem to nonhyperbolic but asymptotically stable equilibria of
vector fields. Moreover, the linearizing topological conjugacy is (i)
defined on the entire basin of attraction if the vector field is
complete, and (ii) a $C^{k\geq 1}$ diffeomorphism on the complement
of the equilibrium if the vector field is $C^k$ and the underlying
space is not $5$-dimensional. We also show that the $C^k$ statement
in the $5$-dimensional case is equivalent to the $4$-dimensional
smooth Poincar\'{e} conjecture.}
}
@ARTICLE{2024_koopman_journal,
AUTHOR = {Z. Liu and N. Ozay and E. D. Sontag},
JOURNAL = {Automatica},
TITLE = {Properties of immersions for systems with multiple limit
sets with implications to learning Koopman embeddings},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {112226},
VOLUME = {176},
KEYWORDS = {linear systems, nonlinear systems, observables,
Koopman embedding, duality},
PDF = {../../FTPDIR/2025_reprint_koopman_liu_ozay_sontag.pdf},
ABSTRACT = {Linear immersions (or Koopman eigenmappings) of a
nonlinear system have wide applications in prediction and control. In
this work, we study the non-existence of one-to-one linear immersions
for nonlinear systems with multiple omega-limit sets. While previous
research has indicated the possibility of discontinuous one-to-one
linear immersions for such systems, it remained uncertain whether
continuous one-to-one linear immersions are attainable. Under mild
conditions, we prove that any continuous one-to-one immersion to a
class of systems including linear systems cannot distinguish
different omega-limit sets, and thus cannot be one-to-one.
Furthermore, we show that this property is also shared by approximate
linear immersions learned from data as sample size increases and
sampling interval decreases. Multiple examples are studied to
illustrate our results.}
}
@ARTICLE{2025_clf_cbf,
AUTHOR = {P. Mestres and J. Corts and E.D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Neural network-based universal formulas for control},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Submitted. Also arXiv https://arxiv.org/abs/2505.24744},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
control-Lyapunov functions, control barrier functions,
universal formulas, neural networks},
ABSTRACT = {We study the problem of designing a controller that
satisfies an arbitrary number of affine inequalities at every point
in the state space. This is motivated by the use of guardrails in
autonomous systems. Indeed, a variety of key control objectives, such
as stability, safety, and input saturation, are guaranteed by
closed-loop systems whose controllers satisfy such inequalities. Many
works in the literature design such controllers as the solution to a
state-dependent quadratic program (QP) whose constraints are
precisely the inequalities. When the input dimension and number of
constraints are high, computing a solution of this QP in real time
can become computationally burdensome. Additionally, the solution of
such optimization problems is not smooth in general, which can
degrade the performance of the system. This paper provides a novel
method to design a smooth controller that satisfies an arbitrary
number of affine constraints. This why we refer to it as a universal
formula for control. The controller is given at every state as the
minimizer of a strictly convex function. To avoid computing the
minimizer of such function in real time, we introduce a method based
on neural networks (NN) to approximate the controller. Remarkably,
this NN can be used to solve the controller design problem for any
task with less than a fixed input dimension and number of affine
constraints, and is completely independent of the state dimension.
Additionally, we show that the NN-based controller only needs to be
trained with datapoints from a compact set in the state space, which
significantly simplifies the training process. Various simulations
showcase the performance of the proposed solution, and also show that
the NN-based controller can be used to warmstart an optimization
scheme that refines the approximation of the true controller in real
time, significantly reducing the computational cost compared to a
generic initialization.}
}
@ARTICLE{2025_voigt_distributed,
AUTHOR = {J.P. Padmakumar and J. Sun 2 and W. Cho 3 and Y. Zhou and
C. Krenz and Zhong Han W.Z and D. Densmore and E. D. Sontag and
C.A. Voigt},
JOURNAL = {Nature Chemical Biology},
TITLE = {Partitioning of a 2-bit hash function across 66
communicating cells},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {268-279},
VOLUME = {21},
KEYWORDS = {synthetic biology, distributed computation,
Boolean functions},
PDF = {../../FTPDIR/2024_nature_chembio_partitioning_padmakumar_et_al_voigt.pdf},
ABSTRACT = {Powerful distributed computing can be achieved by
communicating cells that individually perform simple operations. We
have developed design software to divide a large genetic circuit
across cells as well as the genetic parts to implement the
subcircuits in their genomes. These tools were demonstrated using a
2-bit version of the MD5 hashing algorithm, an early predecessor to
the cryptographic functions underlying cryptocurrency. One iteration
requires 110 logic gates, which were partitioned across 66 strains of
Escherichia coli, requiring the introduction of a total of 1.1 Mb of
recombinant DNA into their genomes. The strains are individually
experimentally verified to integrate their assigned input signals,
process this information correctly, and propagate the result to the
cell in the next layer. This work demonstrates the potential to
obtain programmable control of multicellular biological processes.}
}
@ARTICLE{2024_bispecific,
AUTHOR = {M. Sadeghi and I. Kareva and G. Pogudin and E.D. Sontag},
JOURNAL = {Bulletin of Mathematical Biology},
TITLE = {Quantitative pharmacology methods for bispecific T cell
engagers},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {85-},
VOLUME = {87},
KEYWORDS = {identifiability, model-driven antibody design,
ODE models, quantitative systems pharmacology, systems biology},
PDF = {../../FTPDIR/2025_sadeghi_et_al_bispecific_engagers_bmb_reprint.pdf},
ABSTRACT = {Bispecific T Cell Engagers (BTC) constitute an exciting
antibody design in immuno-oncology that acts to bypass antigen
presentation and forms a direct link between cancer and immune cells
in the tumor microenvironment (TME). By design, BTCs are efficacious
only when the drug is bound to both immune and cancer cell targets,
and therefore approaches to maximize drug-target trimer in the TME
should maximize the drug's efficacy. In this study, we quantitatively
investigate how the concentration of ternary complex and its
distribution depend on both the targets' specific properties and the
design characteristics of the BTC, and specifically on the binding
kinetics of the drug to its targets. A simplified mathematical model
of drug-target interactions is considered here, with insights from
the "three-body" problem applied to the model. Parameter
identifiability analysis performed on the model demonstrates that
steady-state data, which is often available at the early pre-clinical
stages, is sufficient to estimate the binding affinity of the BTC
molecule to both targets. The model is used to analyze several
existing antibodies that are either clinically approved or are under
development, and to explore the common kinetic features. We conclude
with a discussion of the limitations of the BTCs, such as the
increased likelihood of cytokine release syndrome, and an assessment
for a full quantitative pharmacology model that accounts for drug
distribution into the peripheral compartment.},
DOI = {https://doi.org/10.1007/s11538-025-01455-9}
}
@ARTICLE{2025_arxiv_dynamic_phenotypes,
AUTHOR = {E.D. Sontag},
JOURNAL = {arXiv 2512.24946},
TITLE = {Dynamic response phenotypes and model discrimination in
systems and synthetic biology},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Also in Authorea: https://doi.org/10.22541/au.176790592.20368210/v1},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {transient behavior, cumulative dose response,
dose respose, monotone systems, fold-change detection,
scale invariance, reverse engineering, gene networks, cell signaling},
ABSTRACT = {Biological systems encode function not primarily in
steady states, but in the structure of transient responses elicited
by time-varying stimuli. Overshoots, biphasic dynamics, adaptation
kinetics, fold-change detection, entrainment, and cumulative exposure
effects often determine phenotypic outcomes, yet are poorly captured
by classical steady-state or dose-response analyses. This paper
develops an input-output perspective on such "dynamic phenotypes,"
emphasizing how qualitative features of transient behavior constrain
underlying network architectures independently of detailed parameter
values. A central theme is the role of sign structure and
interconnection logic, particularly the contrast between monotone
systems and architectures containing antagonistic pathways. We show
how incoherent feedforward (IFF) motifs provide a simple and
recurrent mechanism for generating non-monotonic and adaptive
responses across multiple levels of biological organization, from
molecular signaling to immune regulation and population dynamics.
Conversely, monotonicity imposes sharp impossibility results that can
be used to falsify entire classes of models from transient data
alone. Beyond step inputs, we highlight how periodic forcing, ramps,
and integral-type readouts such as cumulative dose responses offer
powerful experimental probes that reveal otherwise hidden structure,
separate competing motifs, and expose invariances such as fold-change
detection. Throughout, we illustrate how control-theoretic concepts,
including monotonicity, equivariance, and input-output analysis, can
be used not as engineering metaphors, but as precise mathematical
tools for biological model discrimination. Thus we argue for a shift
in emphasis from asymptotic behavior to transient and input-driven
dynamics as a primary lens for understanding, testing, and
reverse-engineering biological networks.},
DOI = {https://doi.org/10.48550/arXiv.2512.24945}
}
@ARTICLE{sontag2025_trispecific_arxiv,
AUTHOR = {Eduardo D. Sontag},
JOURNAL = {arXiv},
TITLE = {Dynamics of binding three independent ligands to a
single scaffold},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2508.06599},
OPTVOLUME = {},
KEYWORDS = {bispecific antibodies, synthetic biology, immunology,
dCAs9, CRISPR, CRN, chemical reaction networks, complex balanced,
detail balanced},
URL = {https://arxiv.org/abs/2508.06599},
ABSTRACT = {This note considers a system in which three ligands can
independently bind to a scaffold. Such systems arise in diverse
applications, including immunotherapy and synthetic biology. It is
shown that there are unique steady states in each conservation class,
and these are asymptotically stable. The dependency of the
steady-state amount of fully bound complex, as a function of total
scaffold, is analyzed as well.}
}
@ARTICLE{2025_l4dc_talk_paper,
AUTHOR = {E.D. Sontag},
JOURNAL = {arXiv 2507.10452},
TITLE = {Some remarks on gradient dominance and LQR policy
optimization},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, dynamics of algorithms, LQR, reinforcement learning,
machine learning, artificial intelligence, optimal control},
PDF = {../../FTPDIR/2025_l4dc_sontag_arxiv_some_remarks.pdf},
ABSTRACT = {Solutions of optimization problems, including policy
optimization in reinforcement learning, typically rely upon some
variant of gradient descent. There has been much recent work in the
machine learning, control, and optimization communities applying the
Polyak-Łojasiewicz Inequality (PLI) to such problems in order to
establish an exponential rate of convergence (a.k.a. ``linear
convergence'' in the local-iteration language of numerical analysis)
of loss functions to their minima under the gradient flow. Often, as
is the case of policy iteration for the continuous-time LQR problem,
this rate vanishes for large initial conditions, resulting in a mixed
globally linear / locally exponential behavior. This is in sharp
contrast with the discrete-time LQR problem, where there is global
exponential convergence. That gap between CT and DT behaviors
motivates the search for various generalized PLI-like conditions, and
this paper addresses that topic. Moreover, these generalizations are
key to understanding the transient and asymptotic effects of errors
in the estimation of the gradient, errors which might arise from
adversarial attacks, wrong evaluation by an oracle, early stopping of
a simulation, inaccurate and very approximate digital twins,
stochastic computations (algorithm ``reproducibility''), or learning
by sampling from limited data. We describe an ``input to state
stability'' (ISS) analysis of this issue. We also discuss convergence
and PLI-like properties of ``linear feedforward neural networks'' in
feedback control. Much of the work described here was done in
collaboration with Arthur Castello B. de Oliveira, Leilei Cui,
Zhong-Ping Jiang, and Milad Siami. This is a short paper summarizing
the slides presented at my keynote at the 2025 L4DC (Learning for
Dynamics \& Control Conference) in Ann Arbor, Michigan, 05 June 2025.
A partial bibliography has been added.},
DOI = {https://doi.org/10.48550/arXiv.2507.10452}
}
@ARTICLE{tran_et_al_boolean_minimal_heuristic,
AUTHOR = {A.P. Tran and D.D. Jatkar and M.A. Al-Radhawi and
E. Ernst and E.D. Sontag},
JOURNAL = {bioRxiv},
TITLE = {Optimization of heuristic logic synthesis by iteratively
reducing circuit substructures using a database of optimal
implementations},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2025.11.28.691216},
OPTVOLUME = {},
KEYWORDS = {Heuristic logic minimizer, Boolean circuit reduction,
optimal synthesis, logic optimization, synthetic biology},
PUBLISHER = {Cold Spring Harbor Laboratory},
URL = {https://www.biorxiv.org/content/early/2025/11/29/2025.11.28.691216},
ABSTRACT = {Minimal synthesis of Boolean functions is an NP-hard
problem, and heuristic approaches typically give suboptimal circuits.
However, in the emergent field of synthetic biology, genetic logic
designs that use even a single additional Boolean gate can render a
circuit unimplementable in a cell. This has led to a renewed interest
in the field of optimal multilevel Boolean synthesis. For small
numbers (1-4) of inputs, an exhaustive search is possible, but this
is impractical for large circuits. In this work, we demonstrate that
even though it is challenging to build a database of optimal
implementations for anything larger than 4-input Boolean functions, a
database of 4-input optimal implementations can be used to greatly
reduce the number of logical gates required in larger heuristic logic
synthesis implementations. The proposed algorithm combines the
heuristic results with an optimal implementation database and yields
average improvements in fractional gate-count reduction relative to
ABC of 5.16\% for 5-input circuits and 4.54\% for 6-input circuits on
outputs provided by the logic synthesis tool ABC. In addition to the
gains in the efficiency of the implemented circuits, this work also
attests to the importance and practicality of the field of optimal
synthesis, even if it cannot directly provide results for larger
circuits. The focus of this work is on circuits made exclusively of
2-input NOR gates but the presented results are readily applicable to
2-input NAND circuits as well as (2-input) AND/NOT circuits. The
framework proposed here is likely to be adaptable to other types of
circuits. Moreover, a small computational pipeline is provided for
integration with synthetic biology tools such as Cello. An
implementation of the described algorithm, HLM (Hybrid Logic
Minimizer), is available at https://github.com/sontaglab/HLM/.},
DOI = {10.1101/2025.11.28.691216}
}
@ARTICLE{2025_zhang_yalcin_lavaei_sontag_tmlr,
AUTHOR = {H. Zhang and B. Yalcin and J. Lavaei and E.D. Sontag},
JOURNAL = {Transactions on Machine Learning Research},
TITLE = {Exact recovery guarantees for parameterized nonlinear
system identification problem under sparse disturbances or
semi-oblivious attacks},
YEAR = {2025},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-43},
VOLUME = {41-06},
PDF = {../../FTPDIR/zhang_yalcin_lavaei_sontag_exact_recovery_TMLR_2025.pdf},
ABSTRACT = {In this work, we study the problem of learning a
nonlinear dynamical system by parameterizing its dynamics using basis
functions. We assume that disturbances occur at each time step with
an arbitrary probability p, which models the sparsity level of the
disturbance vectors over time. These disturbances are drawn from an
arbitrary, unknown probability distribution, which may depend on past
disturbances, provided that it satisfies a zero-mean assumption. The
primary objective of this paper is to learn the system's dynamics
within a f inite time and analyze the sample complexity as a function
of p. To achieve this, we examine a LASSO-type non-smooth estimator
and establish necessary and sufficient conditions for its
well-specifiedness and the uniqueness of the global solution to the
underlying optimization problem. We then provide exact recovery
guarantees for the estimator under two distinct conditions:
boundedness and Lipschitz continuity of the basis functions. We show
that finite-time exact recovery is achieved with high probability,
even when p approaches 1. Unlike prior works, which primarily focus
on independent and identically distributed (i.i.d.) disturbances and
provide only asymptotic guarantees for system learning, this study
presents the first finite-time analysis of nonlinear dynamical
systems under a highly general disturbance model. Our framework
allows for possible temporal correlations in the disturbances and
accommodates semi-oblivious adversarial attacks, significantly
broadening the scope of existing theoretical results.}
}
@ARTICLE{24submitted_arthur_nn_gradient,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Convergence analysis of overparametrized LQR
formulations},
YEAR = {2025},
OPTMONTH = {},
NOTE = {Version with more details in arXiv 2408.15456},
OPTNUMBER = {},
PAGES = {112504},
VOLUME = {182},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, machine learning, artificial intelligence,
learning theory, singularities in optimization, neural networks,
overparametrization, input to state stability, feedback control, LQR},
PDF = {../../FTPDIR/2025_automatica_olivera_siami_sontag_overparametrized_lqr_reprint.pdf},
ABSTRACT = {Motivated by the growing use of Artificial Intelligence
(AI) tools in control design, this paper takes the first steps
towards bridging the gap between results from Direct Gradient methods
for the Linear Quadratic Regulator (LQR), and neural networks. More
specifically, it looks into the case where one wants to find a Linear
Feed-Forward Neural Network (LFFNN) feedback that minimizes a LQR
cost. This paper starts by computing the gradient formulas for the
parameters of each layer, which are used to derive a key conservation
law of the system. This conservation law is then leveraged to prove
boundedness and global convergence of solutions to critical points,
and invariance of the set of stabilizing networks under the training
dynamics. This is followed by an analysis of the case where the LFFNN
has a single hidden layer. For this case, the paper proves that the
training converges not only to critical points but to the optimal
feedback control law for all but a set of measure-zero of the
initializations. These theoretical results are followed by an
extensive analysis of a simple version of the problem (the ``vector
case''), proving the theoretical properties of accelerated
convergence and robustness for this simpler example. Finally, the
paper presents numerical evidence of faster convergence of the
training of general LFFNNs when compared to traditional direct
gradient methods, showing that the acceleration of the solution is
observable even when the gradient is not explicitly computed but
estimated from evaluations of the cost function.}
}
@INPROCEEDINGS{2025_margal,
AUTHOR = {M. Margaliot and C. Wu and E.D.Sontag},
BOOKTITLE = {Proc. 64th IEEE Conference on Decision and Control (CDC)},
TITLE = {Compact attractors of an antithetic integral feedback
system have a simple structure},
YEAR = {2025},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2880-2885},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {Poincar-Bendixson, synthetic biology,
nonlinear control},
ABSTRACT = {Since its introduction by Briat, Gupta and Khammash, the
antithetic feedback controller design has attracted considerable
attention in both theoretical and experimental systems biology. The
case in which the plant is a two-dimensional linear system (making
the closed-loop system a four-dimensional nonlinear system) has been
analyzed in much detail. This system has a unique equilibrium~$e$
but, depending on parameters, it may exhibit periodic orbits. An
interesting question is for what parameter values periodic orbits
exist. Another open question is whether other dynamical behaviors,
such as chaotic attractors, might be possible for some parameter
choices. We show that, for any parameter choices, every compact
omega-limit set that does not include~$e$ is a periodic solution.
We also show that if the Jacobian of the vector field at the
equilibrium is unstable then a (non-trivial) periodic orbit exists.
The analysis is based on the theory of strongly~$2$-cooperative
systems.}
}
@INPROCEEDINGS{25cdc_miRNA_toggle,
AUTHOR = {N. Nolan and E. Peterman and K. E. Galloway and I. Incer and
E. D. Sontag and Del Vecchio, D.},
BOOKTITLE = {Proc. 64th IEEE Conference on Decision and Control (CDC)},
TITLE = {Guaranteed multistability in a microRNA-based genetic
network by formal methods},
YEAR = {2025},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3043-3048},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {biomolecular systems, systems biology,
synthetic biology, microRNA, toggle switch, contracts theory},
ABSTRACT = {The development of genetic memory devices in synthetic
biology is a challenging process that requires extensive analysis and
characterization. In mammalian systems, this complexity is compounded
by the need for a small DNA payload for efficient delivery into the
cell. Previous genetic memory devices have relied exclusively on
protein-based regulation, which are limited by their large size; in
this paper, we propose a microRNA-based multistable network, which
effectively halves the payload size for more efficient delivery. We
demonstrate that the system can be multistable, and use formal
methods to characterize constraints on design parameters that
guarantee multistability. Our results provide a new genetic network
topology that can achieve multistability and demonstrate the use of
formal methods in the design of sophisticated genetic network
architectures against non-convex top-level specifications.}
}
@INPROCEEDINGS{2025cdc_datadriven_tutorial,
AUTHOR = {M. Sznaier and F. Allgower and de Oliveira, A. C. B. and
N. Ozay and E. D. Sontag},
BOOKTITLE = {Proc. 64th IEEE Conference on Decision and Control (CDC)},
TITLE = {Tutorial: Data driven and learning enabled control},
YEAR = {2025},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2858-2873},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {data-drive control, reinforcement learning},
ABSTRACT = {Data-driven control (DDC), that is the design of
controllers directly from observed data, has attracted substantial
attention in recent years due to its advantages over model-based
control. DDC avoids a computationally expensive, potentially
conservative model identification step and bypasses practically
difficult questions such as model order/class selection. This
tutorial paper seeks to offer a sampling of the different approaches
that have been recently used to synthesize data driven controllers
and filters, covering both analytic approaches and learning enabled
ones, indicating the relative strengths of each. A second objective
is to provide a key to the rapidly expanding literature in the
subject, to help researchers newly interested in this field to
quickly come up to speed.}
}
@INPROCEEDINGS{25cdc_pli,
AUTHOR = {de Oliveira, A.C.B and L. Cui and E. D. Sontag},
BOOKTITLE = {Proc. 64th IEEE Conference on Decision and Control (CDC)},
TITLE = {Remarks on the Polyak-Lojasiewicz inequality and the
convergence of gradient systems},
YEAR = {2025},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Extended version in arXiv:2503.23641},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1150-1155},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, machine learning, artificial intelligence,
numerical methods, dynamics of algorithms, LQR,
reinforcement learning},
PDF = {../../FTPDIR/2025_cdc_oliveira_cui_sontag.pdf},
ABSTRACT = {This work explores generalizations of the
Polyak-Lojasiewicz inequality (PLI) and their implications for the
convergence behavior of gradient flows in optimization problems.
Motivated by the continuous-time linear quadratic regulator (CT-LQR)
policy optimization problem -- where only a weaker version of the PLI
is characterized in the literature -- this work shows that while
weaker conditions are sufficient for global convergence to, and
optimality of the set of critical points of the cost function, the
"profile" of the gradient flow solution can change significantly
depending on which "flavor" of inequality the cost satisfies. After a
general theoretical analysis, we focus on fitting the CT-LQR policy
optimization problem to the proposed framework, showing that, in
fact, it can never satisfy a PLI in its strongest form. We follow up
our analysis with a brief discussion on the difference between
continuous- and discrete-time LQR policy optimization, and end the
paper with some intuition on the extension of this framework to
optimization problems with L1 regularization and solved through
proximal gradient flows.},
DOI = {https://doi.org/10.48550/arXiv.2503.23641}
}
@ARTICLE{cui_jiang_sontag_2023_lqr,
AUTHOR = {L. Cui and Z.P. Jiang and E. D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Small-disturbance input-to-state stability of perturbed
gradient flows: Applications to LQR problem},
YEAR = {2024},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {105804},
VOLUME = {188},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, machine learning, artificial intelligence,
dynamics of algorithms, direct optimization,
input-to-state stability, ISS},
PDF = {../../FTPDIR/2024_scl_cui_jiang_sontag.pdf},
ABSTRACT = {This paper studies the effect of perturbations on the
gradient flow of a general constrained nonlinear programming problem,
where the perturbation may arise from inaccurate gradient estimation
in the setting of data-driven optimization. Under suitable conditions
on the objective function, the perturbed gradient flow is shown to be
small-disturbance input-to-state stable (ISS), which implies that, in
the presence of a small-enough perturbation, the trajectory of the
perturbed gradient flow must eventually enter a small neighborhood of
the optimum. This work was motivated by the question of robustness of
direct methods for the linear quadratic regulator problem, and
specifically the analysis of the effect of perturbations caused by
gradient estimation or round-off errors in policy optimization.
Interestingly, we show small-disturbance ISS for three of the most
common optimization algorithms: standard gradient flow, natural
gradient flow, and Newton gradient flow.},
DOI = {https://doi.org/10.1016/j.sysconle.2024.105804}
}
@ARTICLE{kvalheim_sontag_2023autoencoders,
AUTHOR = {M. D. Kvalheim and E. D. Sontag},
JOURNAL = {Transactions on Machine Learning Research},
TITLE = {Why should autoencoders work?},
YEAR = {2024},
OPTMONTH = {},
NOTE = {See also 2023 preprint in https://arxiv.org/abs/2310.02250.},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence, autoencoders,
neural networks, differential topology, model reduction},
URL = {https://openreview.net/forum?id=uGVFtjvI3v},
PDF = {../../FTPDIR/kvalheim_sontag_autoencoders_TMLR_2024.pdf},
ABSTRACT = {Deep neural network autoencoders are routinely used
computationally for model reduction. They allow recognizing the
intrinsic dimension of data that lie in a k-dimensional subset K of
an input Euclidean space $\R^n$. The underlying idea is to obtain
both an encoding layer that maps $\R^n$ into $\R^k$ (called the
bottleneck layer or the space of latent variables) and a decoding
layer that maps $\R^k$ back into $\R^n$, in such a way that the input
data from the set K is recovered when composing the two maps. This is
achieved by adjusting parameters (weights) in the network to minimize
the discrepancy between the input and the reconstructed output. Since
neural networks (with continuous activation functions) compute
continuous maps, the existence of a network that achieves perfect
reconstruction would imply that K is homeomorphic to a k-dimensional
subset of $\R^k$, so clearly there are topological obstructions to
finding such a network. On the other hand, in practice the technique
is found to "work" well, which leads one to ask if there is a way to
explain this effectiveness. We show that, up to small errors, indeed
the method is guaranteed to work. This is done by appealing to
certain facts from differential geometry. A computational example is
also included to illustrate the ideas.}
}
@ARTICLE{2024_antifragility_arxiv,
AUTHOR = {E.D. Sontag},
JOURNAL = {arXiv},
TITLE = {A concept of antifragility for dynamical systems},
YEAR = {2024},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {antifragility, nonlinear systems, monotone systems,
cancer, systems biology},
URL = {https://doi.org/10.48550/arXiv.2410.17953},
PDF = {../../FTPDIR/2024_11_fragility_sontag_arxiv.pdf},
ABSTRACT = {This paper defines antifragility for dynamical systems
as convexity of a newly introduced "logarithmic rate" of dynamical
systems. It shows how to compute this rate for positive linear
systems, and it interprets antifragility in terms of pulsed
alternations of extreme strategies in comparison to average uniform
strategies.}
}
@ARTICLE{2024_shu_timepoints,
AUTHOR = {S. Wang and M.A. Al-Radhawi and D.A. Lauffenburger and
E.D. Sontag},
JOURNAL = {npj Systems Biology and Applications},
TITLE = {Recovering biomolecular network dynamics from
single-cell omics data requires three time points.},
YEAR = {2024},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {97-},
VOLUME = {10},
KEYWORDS = {machine learning, single-cell data, identifiability,
network reconstruction, dynamical systems},
PDF = {../../FTPDIR/shu.et.al.three.time.points.pdf},
ABSTRACT = {Single-cell omics technologies can measure millions of
cells for up to thousands of biomolecular features, which enables the
data-driven study of highly complex biological networks. However,
these high-throughput experimental techniques often cannot track
individual cells over time, thus complicating the understanding of
dynamics such as the time trajectories of cell states. These
``dynamical phenotypes'' are key to understanding biological
phenomena such as differentiation fates. We show by mathematical
analysis that, in spite of high-dimensionality and lack of individual
cell traces, three timepoints of single-cell omics data are
theoretically necessary and sufficient in order to uniquely determine
the network interaction matrix and associated dynamics. Moreover, we
show through numerical simulations that an interaction matrix can be
accurately determined with three or more timepoints even in the
presence of sampling and measurement noise typical of single-cell
omics. Our results can guide the design of single-cell omics
time-course experiments, and provide a tool for data-driven
phase-space analysis.}
}
@ARTICLE{2024_bennett,
AUTHOR = {de Freitas Magalhes, B. and G. Fan and E.D. Sontag and
K. Josic and M.R. Bennett},
JOURNAL = {ACS Synthetic Biology},
TITLE = {Pattern formation and bistability in a synthetic
intercellular genetic toggle},
YEAR = {2024},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2844-2860},
VOLUME = {13},
KEYWORDS = {synthetic biology, pattern formation, quorum sensing,
systems biology, toggle switch},
PDF = {../../FTPDIR/defreitas_magalhaes-et-al-2024-pattern-formation-and-bistability-in-a-synthetic-intercellular-genetic-toggle_including_s1.pdf},
ABSTRACT = {Differentiation within multicellular organisms is a
complex process that helps to establish spatial patterning and tissue
formation within the body. Often, the differentiation of cells is
governed by morphogens and intercellular signaling molecules that
guide the fate of each cell, frequently using toggle-like regulatory
components. Synthetic biologists have long sought to recapitulate
patterned differentiation with engineered cellular communities, and
various methods for differentiating bacteria have been invented.
Here, we couple a synthetic corepressive toggle switch with
intercellular signaling pathways to create a “quorum-sensing
toggle”. We show that this circuit not only exhibits
population-wide bistability in a well-mixed liquid environment but
also generates patterns of differentiation in colonies grown on agar
containing an externally supplied morphogen. If coupled to other
metabolic processes, circuits such as the one described here would
allow for the engineering of spatially patterned, differentiated
bacteria for use in biomaterials and bioelectronics.}
}
@ARTICLE{2023tac_oliveira_siami_sontag_edges,
AUTHOR = {de Oliveira, A.C.B. and M. Siami and E. D. Sontag},
JOURNAL = {IEEE Transactions on Automatic Control},
TITLE = {Edge selections in bilinear dynamic networks},
YEAR = {2024},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {331-338},
VOLUME = {69},
KEYWORDS = {bilinear systems, networks, robustness},
PDF = {../../FTPDIR/2023_tac_arthur_milad_eduardo_edge-selections-in-bilinear-dynamic.pdf},
ABSTRACT = {We develop some basic principles for the design and
robustness analysis of a continuous-time bilinear dynamical network,
where an attacker can manipulate the strength of the
interconnections/edges between some of the agents/nodes. We formulate
the edge protection optimization problem of picking a limited number
of attack-free edges and minimizing the impact of the attack over the
bilinear dynamical network. In particular, the H2-norm of bilinear
systems is known to capture robustness and performance properties
analogous to its linear counterpart and provides valuable insights
for identifying which edges are most sensitive to attacks. The exact
optimization problem is combinatorial in the number of edges, and
brute-force approaches show poor scalability. However, we show that
the H2-norm as a cost function is supermodular and, therefore, allows
for efficient greedy approximations of the optimal solution. We
illustrate and compare the effectiveness of our theoretical findings
via numerical simulation.},
DOI = {10.1109/TAC.2023.3269323}
}
@INPROCEEDINGS{24cdc_activator_repressor,
AUTHOR = {M. Ali Al-Radhawi and K. Manoj and D. Jatkar and
A. Duvall and Del Vecchio, D. and E.D. Sontag},
BOOKTITLE = {Proc. 63rd IEEE Conference on Decision and Control (CDC)},
TITLE = {Competition for binding targets results in paradoxical
effects for simultaneous activator and repressor action},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5579-5585},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {resource competition, epigenetics, systems biology,
synthetic biology, gene regulatory systems},
PDF = {../../FTPDIR/2024_cdc_competition_repressor_activator_published.pdf},
ABSTRACT = {In the context of epigenetic transformations in cancer
metastasis, a puzzling effect was recently discovered, in which the
elimination (knock-out) of an activating regulatory element leads to
increased (rather than decreased) activity of the element being
regulated. It has been postulated that this paradoxical behavior can
be explained by activating and repressing transcription factors
competing for binding to other possible targets. It is very difficult
to prove this hypothesis in mammalian cells, due to the large number
of potential players and the complexity of endogenous intracellular
regulatory networks. Instead, this paper analyzes this issue through
an analogous synthetic biology construct which aims to reproduce the
paradoxical behavior using standard bacterial gene expression
networks. The paper first reviews the motivating cancer biology work,
and then describes a proposed synthetic construct. A mathematical
model is formulated, and basic properties of uniqueness of steady
states and convergence to equilibria are established, as well as an
identification of parameter regimes which should lead to observing
such paradoxical phenomena (more activator leads to less activity at
steady state). A proof is also given to show that this is a
steady-state property, and for initial transients the phenomenon will
not be observed. This work adds to the general line of work of
resource competition in synthetic circuits.}
}
@INPROCEEDINGS{24cdc_nonexpansive,
AUTHOR = {A. Duvall and E.D. Sontag},
BOOKTITLE = {Proc. 63rd IEEE Conference on Decision and Control (CDC)},
TITLE = {A remark on omega limit sets for non-expansive dynamics},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1504-1511},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractive systems, contractions,
non-expansive systems},
PDF = {../../FTPDIR/2024_cdc_nonexpansive_published.pdf},
ABSTRACT = {In this paper, we study systems of time-invariant
ordinary differential equations whose flows are non-expansive with
respect to a norm, meaning that the distance between solutions may
not increase. Since non-expansiveness (and contractivity) are
norm-dependent notions, the topology of $\omega$-limit sets of
solutions may depend on the norm. For example, and at least for
systems defined by real-analytic vector fields, the only possible
$\omega$-limit sets of systems that are non-expansive with respect to
polyhedral norms (such as $\ell^p$ norms with $p =1$ or $p=\infty$)
are equilibria. In contrast, for non-expansive systems with respect
to Euclidean ($\ell^2$) norm, other limit sets may arise (such as
multi-dimensional tori): for example linear harmonic oscillators are
non-expansive (and even isometric) flows, yet have periodic orbits as
$\omega$-limit sets. This paper shows that the Euclidean linear case
is what can be expected in general: for flows that are non-expansive
with respect to any strictly convex norm (such as $\ell^p$ for any
$p\not=1,\infty$), and if there is at least one bounded solution,
then the $\omega$-limit set of every trajectory is also an omega
limit set of a linear time-invariant system.}
}
@INPROCEEDINGS{duvall_sontag_2023_arxiv_ges_contractions,
AUTHOR = {A. Duvall and E. D. Sontag},
BOOKTITLE = {Proc. 2024 Automatic Control Conference},
TITLE = {Global exponential stability or contraction of an
unforced system do not imply entrainment to periodic inputs},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Also preprint in arXiv:2310.03241.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1837-1842},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractive systems, contractions,
non-expansive systems},
PDF = {../../FTPDIR/2024_acc_global_exponential_contracting.pdf},
ABSTRACT = {It is often of interest to know which systems will
approach a periodic trajectory when given a periodic input. Results
are available for certain classes of systems, such as contracting
systems, showing that they always entrain to periodic inputs. In
contrast to this, we demonstrate that there exist systems which are
globally exponentially stable yet do not entrain to a periodic input.
This could be seen as surprising, as it is known that globally
exponentially stable systems are in fact contracting with respect to
some Riemannian metric. The paper also addresses the broader issue of
entrainment when an input is added to a contractive system.}
}
@INPROCEEDINGS{24cdc_contracts,
AUTHOR = {I. Incer and A. Pandey and E. Peterson and N. Nolan and
K. E. Galloway and R. M. Murray and E. D. Sontag and Del Vecchio, D.},
BOOKTITLE = {Proc. 2024 63rd IEEE Conference on Decision and Control (CDC)},
TITLE = {Guaranteeing system-level properties in genetic circuits
subject to context effects},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5558-5565},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {synthetic biology, systems biology,
resource constraints, contracts theory},
PDF = {../../FTPDIR/2024_cdc_contracts_published.pdf},
ABSTRACT = {The identification of constraints on system parameters
that will ensure that a system achieves desired requirements remains
a challenge in synthetic biology, where components unintendedly
affect one another by perturbing the cellular environment in which
they operate. This paper shows how to solve this problem optimally
for a class of input/output system-level specifications, and for
unintended interactions due to resource sharing. Specifically, we
show how to solve the problem based on the input/output properties of
the subsystems and on the unintended interaction map. Our approach is
based on the elimination of quantifiers in monotone properties of the
system. We illustrate applications of this methodology to
guaranteeing system-level performance of multiplexed and sequential
biosensing and of bistable genetic circuits.}
}
@INPROCEEDINGS{24cdc_polly_wu,
AUTHOR = {P. Yu and E.D. Sontag},
BOOKTITLE = {Proc. 2024 63rd IEEE Conference on Decision and Control (CDC)},
TITLE = {A necessary condition for non-monotonic dose response,
with an application to a kinetic proofreading model},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Note: there is an extended version in arXiv; also, a journal paper is in preparation.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4823-4829},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, IFFL, dose response},
PDF = {../../FTPDIR/2024_cdc_iffl_final.pdf},
ABSTRACT = {Steady state non-monotonic ("biphasic") dose responses
are often observed in experimental biology, which raises the control
theoretic question of identifying which possible mechanisms might
underlie such behaviors. It is well known that the presence of an
incoherent feedforward loop (IFFL) in a network may give rise to a
non-monotonic response, and it has been informally conjectured that
this condition is also necessary. However, this conjecture has been
disproved with an example of a system in which input and output nodes
are the same. In this paper, we show that the converse implication
does hold when the input and output are distinct. Towards this aim,
we give necessary and sufficient conditions for when minors of a
symbolic matrix have mixed signs. Finally, we study in full
generality when a model of immune T-cell activation could exhibit a
steady state non-monotonic dose response.}
}
@INPROCEEDINGS{24cdc_arthur_nn_gradient,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
BOOKTITLE = {Proc. 2024 63rd IEEE Conference on Decision and Control (CDC)},
TITLE = {Remarks on the gradient training of linear neural
network based feedback for the LQR Problem},
YEAR = {2024},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {7846-7852},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dynamics, gradient descent, gradient systems,
numerical methods, dynamics of algorithms, gradient dominance,
gradient flows, machine learning, artificial intelligence,
neural networks, overparametrization, dynamics of algorithms,
input to state stability, feedback control, LQR},
PDF = {../../FTPDIR/2024_cdc_lqr_overparametrized_published.pdf},
ABSTRACT = {Motivated by the current interest in using Artificial
intelligence (AI) tools in control design, this paper takes the first
steps towards bridging results from gradient methods for solving the
LQR control problem, and neural networks. More specifically, it looks
into the case where one wants to find a Linear Feed-Forward Neural
Network (LFFNN) that minimizes the Linear Quadratic Regulator (LQR)
cost. This work develops gradient formulas that can be used to
implement the training of LFFNNs to solve the LQR problem, and
derives an important conservation law of the system. This
conservation law is then leveraged to prove global convergence of
solutions and invariance of the set of stabilizing networks under the
training dynamics. These theoretical results are then followed by and
extensive analysis of the simplest version of the problem (the
``scalar case'') and by numerical evidence of faster convergence of
the training of general LFFNNs when compared to traditional direct
gradient methods. These results not only serve as indication of the
theoretical value of studying such a problem, but also of the
practical value of LFFNNs as design tools for data-driven control
applications.}
}
@ARTICLE{MAli_competition_phenotypes,
AUTHOR = {M.A. Al-Radhawi and Del Vecchio, D. and E.D. Sontag},
JOURNAL = {IEEE Control Systems Letters},
TITLE = {Identifying competition phenotypes in synthetic
biochemical circuits},
YEAR = {2023},
OPTMONTH = {},
NOTE = {(Online published in 2022; in print 2023.)},
OPTNUMBER = {},
PAGES = {211-216},
VOLUME = {7},
KEYWORDS = {Resource competition, model discrimination,
synthetic biology, system identification},
PDF = {../../FTPDIR/2022_ieee_letters_competition_phenotypes.pdf},
ABSTRACT = {Synthetic gene circuits require cellular resources,
which are often limited. This leads to competition for resources by
different genes, which alter a synthetic genetic circuit's behavior.
However, the manner in which competition impacts behavior depends on
the identity of the "bottleneck" resource which might be difficult to
discern from input-output data. In this paper, we aim at classifying
the mathematical structures of resource competition in biochemical
circuits. We find that some competition structures can be
distinguished by their response to different competitors or resource
levels. Specifically, we show that some response curves are always
linear, convex, or concave. Furthermore, high levels of certain
resources protect the behavior from low competition, while others do
not. We also show that competition phenotypes respond differently to
various interventions. Such differences can be used to eliminate
candidate competition mechanisms when constructing models based on
given data. On the other hand, we show that different networks can
display mathematically equivalent competition phenotypes.}
}
@ARTICLE{2022_shu_2d,
AUTHOR = {S. Wang and E.D. Sontag and D.A. Lauffenburger},
JOURNAL = {Cell Systems},
TITLE = {What cannot be seen correctly in 2D visualizations of
single-cell `omics data?},
YEAR = {2023},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {723-731},
VOLUME = {14},
KEYWORDS = {visualization, single-cell data, tSNE, UMAP},
URL = {https://doi.org/10.1016/j.cels.2023.07.002},
PDF = {../../FTPDIR/2023_cell_systems_visualization_wang_sontag_lauffenburger.pdf},
ABSTRACT = {Single-cell -omics datasets are high-dimensional and
difficult to visualize. A common strategy for exploring such data is
to create and analyze 2D projections. Such projections may be highly
nonlinear, and implementation algorithms are designed with the goal
of preserving aspects of the original high-dimensional shape of data
such as neighborhood relationships or metrics. However, important
aspects of high-dimensional geometry are known from mathematical
theory to have no equivalent representation in 2D, or are subject to
large distortions, and will therefore be misrepresented or even
invisible in any possible 2D representation. We show that features
such as quantitative distances, relative positioning, and qualitative
neighborhoods of high-dimensional data points will always be
misrepresented in 2D projections. Our results rely upon concepts from
differential geometry, combinatorial geometry, and algebraic
topology. As an illustrative example, we show that even a simple
single-cell RNA sequencing dataset will always be distorted, no
matter what 2D projection is employed. We also discuss how certain
recently developed computational tools can help describe the
high-dimensional geometric features that will be necessarily missing
from any possible 2D projections.}
}
@INPROCEEDINGS{2023_ifac_koopman,
AUTHOR = {Z. Liu and N. Ozay and E. D. Sontag},
BOOKTITLE = {22nd IFAC World Congress, IFAC-PapersOnLine},
TITLE = {On the non-existence of immersions for systems with
multiple omega-limit sets},
YEAR = {2023},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {This is a preliminary version of the journal paper Properties of immersions for systems with multiple limit sets with implications to learning Koopman embeddings.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {60-64},
OPTPUBLISHER = {},
OPTSERIES = {},
VOLUME = {56},
KEYWORDS = {linear systems, nonlinear systems, observables,
Koopman embedding, duality},
PDF = {../../FTPDIR/2023_ifac_koopman_liu_ozay_sontag.pdf},
ABSTRACT = {Linear immersions (or Koopman eigenmappings) of a
nonlinear system have wide applications in prediction and control. In
this work, we study the existence of one-to-one linear immersions for
nonlinear systems with multiple omega-limit sets. For this class of
systems, existing work shows that a discontinuous one-to-one linear
immersion may exist, but it is unclear if a continuous one-to-one
linear immersion exists. Under mild conditions, we prove that systems
with multiple omega-limit sets cannot admit a continuous one-to-one
immersion to a class of systems including linear systems.},
DOI = {https://doi.org/10.1016/j.ifacol.2023.10.1408}
}
@INPROCEEDINGS{23cdc_brancodeoliveira_siami_sontag,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
BOOKTITLE = {Proc. 2023 62st IEEE Conference on Decision and Control (CDC)},
TITLE = {Dynamics and perturbations of overparameterized linear
neural networks},
YEAR = {2023},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Extended version is On the ISS property of the gradient flow for single hidden-layer neural networks with linear activations, arXiv https://arxiv.org/abs/2305.09904},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {7356-7361},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {gradient dominance, neural networks,
overparametrization, gradient descent, gradient dynamics,
gradient descent, gradient systems, gradient descent,
numerical methods, dynamics of algorithms, input to state stability,
gradient systems},
PDF = {../../FTPDIR/23cdc_brancodeoliveira_siami_sontag_neural_linear.pdf},
ABSTRACT = {Recent research in neural networks and machine learning
suggests that using many more parameters than strictly required by
the initial complexity of a regression problem can result in more
accurate or faster-converging models -- contrary to classical
statistical belief. This phenomenon, sometimes known as ``benign
overfitting'', raises questions regarding in what other ways might
overparameterization affect the properties of a learning problem. In
this work, we investigate the effects of overfitting on the
robustness of gradient-descent training when subject to uncertainty
on the gradient estimation. This uncertainty arises naturally if the
gradient is estimated from noisy data or directly measured. Our
object of study is a linear neural network with a single, arbitrarily
wide, hidden layer and an arbitrary number of inputs and outputs. In
this paper we solve the problem for the case where the input and
output of our neural-network are one-dimensional, deriving sufficient
conditions for robustness of our system based on necessary and
sufficient conditions for convergence in the undisturbed case. We
then show that the general overparametrized formulation introduces a
set of spurious equilibria which lay outside the set where the loss
function is minimized, and discuss directions of future work that
might extend our current results for more general formulations. },
DOI = {10.1109/CDC49753.2023.10383478}
}
@INCOLLECTION{2019_EMT_MET_bookchapter,
AUTHOR = {M.A. Al-Radhawi and E.D. Sontag},
BOOKTITLE = {Realization and model reduction of dynamical systems},
PUBLISHER = {Springer Nature},
TITLE = {Analysis of a reduced model of epithelial-mesenchymal
fate determination in cancer metastasis as a singularly-perturbed
monotone system},
YEAR = {2022},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C.A. Beattie and P. Benner and M. Embree and S. Gugercin and
S. Lefteriu},
OPTMONTH = {},
NOTE = {(Previous version: 2020 preprint in arXiv:1910.11311.)},
OPTNUMBER = {},
OPTPAGES = {},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {epithelial-mesenchymal transition, miRNA,
singular perturbations, monotone systems, oncology, cancer,
metastasis, reaction networks, reaction networks, systems biology},
PDF = {../../FTPDIR/2022_al-radhawi_sontag_epithelial_mesenchymal_singularly_perturbed.pdf},
ABSTRACT = {Metastasis can occur after malignant cells transition
from the epithelial phenotype to the mesenchymal phenotype. This
transformation allows cells to migrate via the circulatory system and
subsequently settle in distant organs after undergoing the reverse
transition. The core gene regulatory network controlling these
transitions consists of a system made up of coupled SNAIL/miRNA-34
and ZEB1/miRNA-200 subsystems. In this work, we formulate a
mathematical model and analyze its long-term behavior. We start by
developing a detailed reaction network with 24 state variables.
Assuming fast promoter and mRNA kinetics, we then show how to reduce
our model to a monotone four-dimensional system. For the reduced
system, monotone dynamical systems theory can be used to prove
generic convergence to the set of equilibria for all bounded
trajectories. The theory does not apply to the full model, which is
not monotone, but we briefly discuss results for singularly-perturbed
monotone systems that provide a tool to extend convergence results
from reduced to full systems, under appropriate time separation
assumptions.}
}
@ARTICLE{alradhawi_sadeghi_sontag_cdc2021_covid,
AUTHOR = {M.A. Al-Radhawi and M. Sadeghi and E.D. Sontag},
JOURNAL = {IEEE Control Systems Letters},
TITLE = {Long-term regulation of prolonged epidemic outbreaks in
large populations via adaptive control: a singular perturbation
approach},
YEAR = {2022},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {578-583},
VOLUME = {6},
KEYWORDS = {epidemiology, COVID-19, COVID, systems biology},
PDF = {../../FTPDIR/2021_mali_sadeghi_sontag_covid_qss.pdf},
ABSTRACT = {In order to control highly-contagious and prolonged
outbreaks, public health authorities intervene to institute social
distancing, lock-down policies, and other Non-Pharmaceutical
Interventions (NPIs). Given the high social, educational,
psychological, and economic costs of NPIs, authorities tune them,
alternatively tightening up or relaxing rules, with the result that,
in effect, a relatively flat infection rate results. For example,
during the summer of 2020 in parts of the United States, daily
COVID-19 infection numbers dropped to a plateau. This paper
approaches NPI tuning as a control-theoretic problem, starting from a
simple dynamic model for social distancing based on the classical SIR
epidemics model. Using a singular-perturbation approach, the plateau
becomes a Quasi-Steady-State (QSS) of a reduced two-dimensional SIR
model regulated by adaptive dynamic feedback. It is shown that the
QSS can be assigned and it is globally asymptotically stable.
Interestingly, the dynamic model for social distancing can be
interpreted as a nonlinear integral controller. Problems of data
fitting and parameter identifiability are also studied for this
model. This letter also discusses how this simple model allows for a
meaningful study of the effect of population size, vaccinations, and
the emergence of second waves.}
}
@ARTICLE{MAli_EMT_2022,
AUTHOR = {M.A. Al-Radhawi and S. Tripathi and Y. Zhang and
E.D. Sontag and H. Levine},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Epigenetic factor competition reshapes the EMT landscape},
YEAR = {2022},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e2210844119},
VOLUME = {119},
KEYWORDS = {gene networks, Epithelial-Mesenchymal Transition, EMT,
epigenetics, systems biology, cancer},
URL = {https://doi.org/10.1073/pnas.2210844119},
PDF = {../../FTPDIR/2022_al-radhawi_tripathi_sontag_levine_epigenetic_factors_emt_with_SI.pdf},
ABSTRACT = {The emergence of and transitions between distinct
phenotypes in isogenic cells can be attributed to the intricate
interplay of epigenetic marks, external signals, and gene regulatory
elements. These elements include chromatin remodelers, histone
modifiers, transcription factors, and regulatory RNAs. Mathematical
models known as Gene Regulatory Networks (GRNs) are an increasingly
important tool to unravel the workings of such complex networks. In
such models, epigenetic factors are usually proposed to act on the
chromatin regions directly involved in the expression of relevant
genes. However, it has been well-established that these factors
operate globally and compete with each other for targets genome-wide.
Therefore, a perturbation of the activity of a regulator can
redistribute epigenetic marks across the genome and modulate the
levels of competing regulators. In this paper, we propose a
conceptual and mathematical modeling framework that incorporates both
local and global competition effects between antagonistic epigenetic
regulators in addition to local transcription factors, and show the
counter-intuitive consequences of such interactions. We apply our
approach to recent experimental findings on the
Epithelial-Mesenchymal Transition (EMT). We show that it can explain
the puzzling experimental data as well provide new verifiable
predictions.}
}
@ARTICLE{angeli_alradhawi_sontag_2020robust,
AUTHOR = {D. Angeli and M.A. Al-Radhawi and E.D. Sontag},
JOURNAL = {IEEE Transactions on Automatic Control},
TITLE = {A robust Lyapunov criterion for non-oscillatory
behaviors in biological interaction networks},
YEAR = {2022},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {7},
PAGES = {3305-3320},
VOLUME = {67},
KEYWORDS = {contractive systems, contractions, oscillations,
dynamical systems, enzymatic cycles, systems biology},
PDF = {../../FTPDIR/angeli_alradhawi_sontag_2022robust.pdf},
ABSTRACT = {This paper introduces a notion of non-oscillation,
proposes a constructive method for its robust verification, and
studies its application to biological interaction networks. The paper
starts by revisiting Muldowney's result on non-existence of periodic
solutions based on the study of the variational system of the second
additive compound of the Jacobian of a nonlinear system. It then
shows that exponential stability of the latter rules out limit
cycles, quasi-periodic solutions, and broad classes of oscillatory
behavior. The focus then turns ton nonlinear equations arising in
biological interaction networks with general kinetics, the paper
shows that the dynamics of the variational system can be embedded in
a linear differential inclusion. This leads to algorithms for
constructing piecewise linear Lyapunov functions to certify global
robust non-oscillatory behavior. Finally, the paper applies the new
techniques to study several regulated enzymatic cycles where
available methods are not able to provide any information about their
qualitative global behavior.},
DOI = {10.1109/TAC.2021.3096807}
}
@ARTICLE{22_annual_reviews_tutorial_imp,
AUTHOR = {M. Bin and J. Huang and A. Isidori and L. Marconi and
M. Mischiati and E. D. Sontag},
JOURNAL = {Annual Review of Control, Robotics, and Autonomous Systems},
TITLE = {Internal models in control, bioengineering, and
neuroscience},
YEAR = {2022},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {20.1-20.25},
VOLUME = {5},
KEYWORDS = {feeedback, internal model principle, nonlinear systems},
PDF = {../../FTPDIR/bin_et_al_internal_model_annual_reviews_internal_models_galleys.pdf},
ABSTRACT = {Internal models are nowadays customarily used in
different domains of science and engineering to describe how living
organisms or artificial computational units embed their acquired
knowledge about recurring events taking place in the surrounding
environment. This article reviews the internal model principle in
control theory, bioengineering, and neuroscience, illustrating the
fundamental concepts and theoretical developments of the last few
decades of research.}
}
@ARTICLE{sontag2022iss_gradient_flows,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Remarks on input to state stability of perturbed
gradient flows, motivated by model-free feedback control learning},
YEAR = {2022},
OPTMONTH = {},
NOTE = {Important: there is an error in the paper. For the LQR application, the paper only shows iISS, not ISS. See the paper Small-disturbance input-to-state stability of perturbed gradient flows: Applications to LQR problem for details.},
OPTNUMBER = {},
PAGES = {105138},
VOLUME = {161},
KEYWORDS = {gradient dominance, iss, input to state stability,
data-driven control, gradient systems, steepest descent,
model-free control, gradient dynamics, gradient descent,
gradient systems, gradient descent, numerical methods,
dynamics of algorithms},
PDF = {../../FTPDIR/iss_gradient_reprint_2022.pdf},
ABSTRACT = {Recent work on data-driven control and reinforcement
learning has renewed interest in a relatively old field in control
theory: model-free optimal control approaches which work directly
with a cost function and do not rely upon perfect knowledge of a
system model. Instead, an "oracle" returns an estimate of the cost
associated to, for example, a proposed linear feedback law to solve a
linear-quadratic regulator problem. This estimate, and an estimate of
the gradient of the cost, might be obtained by performing experiments
on the physical system being controlled. This motivates in turn the
analysis of steepest descent algorithms and their associated gradient
differential equations. This paper studies the effect of errors in
the estimation of the gradient, framed in the language of input to
state stability, where the input represents a perturbation from the
true gradient. Since one needs to study systems evolving on proper
open subsets of Euclidean space, a self-contained review of input to
state stability definitions and theorems for systems that evolve on
such sets is included. The results are then applied to the study of
noisy gradient systems, as well as the associated steepest descent
algorithms.}
}
@ARTICLE{2022_sontag_biswas_cowan_arxiv,
AUTHOR = {E.D. Sontag and D. Biswas and N.J. Cowan},
JOURNAL = {arXiv},
TITLE = {An observability result related to active sensing},
YEAR = {2022},
OPTMONTH = {},
NOTE = {arXiv 2210.03848},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {nonlinear systems, observability, active sensing},
PDF = {../../FTPDIR/sontag_biswas_cowan_active_sensing_arxiv_10.48550_arxiv.2210.03848.pdf},
ABSTRACT = {For a general class of translationally invariant systems
with a specific category of nonlinearity in the output, this paper
presents necessary and sufficient conditions for global
observability. Critically, this class of systems cannot be stabilized
to an isolated equilibrium point by dynamic output feedback. These
analyses may help explain the active sensing movements made by
animals when they perform certain motor behaviors, despite the fact
that these active sensing movements appear to run counter to the
primary motor goals. The findings presented here establish that
active sensing underlies the maintenance of observability for such
biological systems, which are inherently nonlinear due to the
presence of the high-pass sensor dynamics.}
}
@INPROCEEDINGS{greene_sontag_nonzero_lockdown,
AUTHOR = {J M Greene and E D Sontag},
BOOKTITLE = {Proc. 2022 Automatic Control Conference},
TITLE = {Minimizing the infected peak utilizing a single
lockdown: a technical result regarding equal peaks},
YEAR = {2022},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3640-3647},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {epidemiology, COVID-19, COVID, systems biology},
PDF = {../../FTPDIR/2022_greene_sontag_minimizing_the_infected_peak_utilizing_a_single_lockdown_a_technical_result_regarding_equal_peaks.pdf},
ABSTRACT = {Due to the usage of social distancing as a means to
control the spread of the novel coronavirus disease COVID-19, there
has been a large amount of research into the dynamics of
epidemiological models with time-varying transmission rates. Such
studies attempt to capture population responses to differing levels
of social distancing, and are used for designing policies which both
inhibit disease spread but also allow for limited economic activity.
One common criterion utilized for the recent pandemic is the peak of
the infected population, a measure of the strain placed upon the
health care system; protocols which reduce this peak are commonly
said to "flatten the curve". In this work, we consider a very
specialized distancing mandate, which consists of one period of fixed
length of distancing, and addresses the question of optimal
initiation time. We prove rigorously that this time is characterized
by an equal peaks phenomenon: the optimal protocol will experience a
rebound in the infected peak after distancing is relaxed, which is
equal in size to the peak when distancing is commenced. In the case
of a non-perfect lockdown (i.e. disease transmission is not
completely suppressed), explicit formulas for the initiation time
cannot be computed, but implicit relations are provided which can be
pre-computed given the current state of the epidemic. Expected
extensions to more general distancing policies are also hypothesized,
which suggest designs for the optimal timing of non-overlapping
lockdowns.}
}
@INPROCEEDINGS{2022_sznaier_olshevsky_sontag_mtns_control_oriented_learning,
AUTHOR = {M. Sznaier and A. Olshevsky and E.D. Sontag},
BOOKTITLE = {Proc. 25th Int. Symp. Mathematical Theory of Networks and Systems (MTNS 2022)},
TITLE = {The role of systems theory in control oriented learning},
YEAR = {2022},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Looks like only the abstract was published!},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control oriented learning, neural networks,
reinforcement learning, feedback control, machine learning},
PDF = {../../FTPDIR/2022_sznaier_olshevsky_sontag_mtns_control_oriented_learning.pdf},
ABSTRACT = {Systems theory can play an important in unveiling
fundamental limitations of learning algorithms and architectures when
used to control a dynamical system, and in suggesting strategies for
overcoming these limitations. As an example, a feedforward neural
network cannot stabilize a double integrator using output feedback.
Similarly, a recurrent NN with differentiable activation functions
that stabilizes a non-strongly stabilizable system must be itself
open loop unstable, a fact that has profound implications for
training with noisy, finite data. A potential solution to this
problem, motivated by results on stabilization with periodic control,
is the use of neural nets with periodic resets, showing that indeed
systems theoretic analysis is instrumental in developing
architectures capable of controlling certain classes of unstable
systems. This short conference paper also argues that when the goal
is to learn control oriented models, the loss function should reflect
closed loop, rather than open loop model performance, a fact that can
be accomplished by using gap-metric motivated loss functions.}
}
@INPROCEEDINGS{22cdc_brancodeoliveira_siami_sontag,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
BOOKTITLE = {Proc. 2022 61st IEEE Conference on Decision and Control (CDC)},
TITLE = {Sensor and actuator scheduling in bilinear dynamical
networks},
YEAR = {2022},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {WeCT09.4},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/22cdc_brancodeoliveira_siami_sontag.pdf},
ABSTRACT = {In this paper, we investigate the problem of finding a
sparse sensor and actuator (S/A) schedule that minimizes the
approximation error between the input-output behavior of a fully
sensed/actuated bilinear system and the system with the scheduling.
The quality of this approximation is measuredby an H2-like metric,
which is defined for a bilinear (time-varying) system with S/A
scheduling based on the discrete Laplace transform of its Volterra
kernels. First, we discuss the difficulties of designing S/A
schedules for bilinear systems, which prevented us from finding a
polynomial time algorithmfor solving the problem. We then propose a
polynomial-time S/A scheduling heuristic that selects a fraction of
sensors and node actuators at each time step while maintaining a
small approximation error between the input-output behavior of
thefully sensed/actuated system and the one with S/A scheduling in
this H2-based sense. Numerical experiments illustrate the good
approximation quality of our proposed methods.}
}
@ARTICLE{2021_open_society_maximizing_throughput,
AUTHOR = {M.A. Al-Radhawi and M. Margaliot and E. D. Sontag},
JOURNAL = {Royal Society Open Science},
TITLE = {Maximizing average throughput in oscillatory biochemical
synthesis systems: an optimal control approach},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {9},
PAGES = {210878},
VOLUME = {8},
PDF = {../../FTPDIR/2021_royal_open_al-radhawi_margaliot_sontag_maximizing_throughput.pdf},
ABSTRACT = { A dynamical system entrains to a periodic input if its
state converges globally to an attractor with the same period. In
particular, for a constant input, the state converges to a unique
equilibrium point for any initial condition. We consider the problem
of maximizing a weighted average of the system's output along the
periodic attractor. The gain of entrainment is the benefit achieved
by using a non-constant periodic input relative to a constant input
with the same time average. Such a problem amounts to optimal
allocation of resources in a periodic manner. We formulate this
problem as a periodic optimal control problem, which can be analyzed
by means of the Pontryagin maximum principle or solved numerically
via powerful software packages. We then apply our framework to a
class of nonlinear occupancy models that appear frequently in
biological synthesis systems and other applications. We show that,
perhaps surprisingly, constant inputs are optimal for various
architectures. This suggests that the presence of non-constant
periodic signals, which frequently appear in biological occupancy
systems, is a signature of an underlying time-varying objective
functional being optimized. }
}
@ARTICLE{chen_et_al_sontag_counter_2021,
AUTHOR = {T. Chen and M. A. Al-Radhawi and C.A. Voigt and
E.D. Sontag},
JOURNAL = {iScience},
TITLE = {A synthetic distributed genetic multi-bit counter},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {103526},
VOLUME = {24},
KEYWORDS = {counters, synthetic biology, transcriptional networks,
gene networks, boolean circuits, boolean gates, systems biology},
PDF = {../../FTPDIR/chen_alradhawi_voigt_sontag_counter_iscience_including_SI.pdf},
ABSTRACT = {A design for genetically-encoded counters is proposed
via repressor-based circuits. An N-bit counter reads sequences of
input pulses and displays the total number of pulses, modulo $2^N$.
The design is based on distributed computation, with specialized cell
types allocated to specific tasks. This allows scalability and
bypasses constraints on the maximal number of circuit genes per cell
due to toxicity or failures due to resource limitations. The design
starts with a single-bit counter. The N-bit counter is then obtained
by interconnecting (using diffusible chemicals) a set of N single-bit
counters and connector modules. An optimization framework is used to
determine appropriate gate parameters and to compute bounds on
admissible pulse widths and relaxation (inter-pulse) times, as well
as to guide the construction of novel gates. This work can be viewed
as a step toward obtaining circuits that are capable of
finite-automaton computation, in analogy to digital central
processing units.}
}
@ARTICLE{hanson_raginsky_sontag_learn_rnn,
AUTHOR = {J. Hanson and M. Raginsky and E.D. Sontag},
JOURNAL = {Proc. of Machine Learning Research},
TITLE = {Learning recurrent neural net models of nonlinear
systems},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-11},
VOLUME = {144},
KEYWORDS = {machine learning, artificial intelligence,
empirical risk minimization, recurrent neural networks,
dynamical systems, continuous time, system identification,
statistical learning theory, generalization bounds},
PDF = {../../FTPDIR/hanson_raginsky_sontag_machine_learning_research_2021.pdf},
ABSTRACT = {This paper considers the following learning problem:
given sample pairs of input and output signals generated by an
unknown nonlinear system (which is not assumed to be causal or
time-invariant), one wishes to find a continuous-time recurrent
neural net, with activation function tanh, that approximately
reproduces the underlying i/o behavior with high confidence.
Leveraging earlier work concerned with matching derivatives up to a
finite order of the input and output signals the problem is
reformulated in familiar system-theoretic language and quantitative
guarantees on the sup-norm risk of the learned model are derived, in
terms of the number of neurons, the sample size, the number of
derivatives being matched, and the regularity properties of the
inputs, the outputs, and the unknown i/o map.}
}
@ARTICLE{special_issue_annual_reviews_epidemics2,
AUTHOR = {E. A. Hernandez-Vargas and G. Giordano and E.D. Sontag and
J. G. Chase and H. Chang and A. Astolfi},
JOURNAL = {Annual Reviews in Control},
TITLE = {Second special section on systems and control research
efforts against COVID-19 and future pandemics},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {424-425},
VOLUME = {51},
KEYWORDS = {COVID-19, epidemiology, epidemics},
URL = {https://www.sciencedirect.com/science/article/pii/S1367578821000225},
DOI = {https://doi.org/10.1016/j.arcontrol.2021.04.005}
}
@ARTICLE{special_issue_annual_reviews_epidemics3,
AUTHOR = {E. A. Hernandez-Vargas and G. Giordano and E.D. Sontag and
J. G. Chase and H. Chang and A. Astolfi},
JOURNAL = {Annual Reviews in Control},
TITLE = {Third special section on systems and control research
efforts against COVID-19 and future pandemics},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {446-447},
VOLUME = {52},
KEYWORDS = {COVID-19, epidemiology, epidemics},
URL = {https://www.sciencedirect.com/science/article/pii/S1367578821000900},
DOI = {https://doi.org/10.1016/j.arcontrol.2021.10.015}
}
@ARTICLE{hong_et_al_kim_2020,
AUTHOR = {H. Hong and J. Kim and M.A. Al-Radhawi and E.D. Sontag and
J. K. Kim},
JOURNAL = {Communications Biology},
TITLE = {Derivation of stationary distributions of biochemical
reaction networks via structure transformation},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {620-},
VOLUME = {4},
KEYWORDS = {stationary distribution, reaction networks,
network translation, reaction networks, chemical master equation,
stochastic, probabilistic, systems biology},
PDF = {../../FTPDIR/2021_communications_biology_hong_kim_al-radhawi_sontag_kim_stochastic_structure_transformation_including_SI.pdf},
ABSTRACT = {Long-term behaviors of biochemical reaction networks
(BRNs) are described by steady states in deterministic models and
stationary distributions in stochastic models. Unlike deterministic
steady states, stationary distributions capturing inherent
fluctuations of reactions are extremely difficult to derive
analytically due to the curse of dimensionality. Here, we develop a
method to derive analytic stationary distributions from deterministic
steady states by transforming BRNs to have a special dynamic
property, called complex balancing. Specifically, we merge nodes and
edges of BRNs to match in- and out-flows of each node. This allows us
to derive the stationary distributions of a large class of BRNs,
including autophosphorylation networks of EGFR, PAK1, and Aurora B
kinase and a genetic toggle switch. This reveals the unique
properties of their stochastic dynamics such as robustness,
sensitivity, and multimodality. Importantly, we provide a
user-friendly computational package, CASTANET, that automatically
derives symbolic expressions of the stationary distributions of BRNs
to understand their long-term stochasticity.}
}
@ARTICLE{johnson_et_al_brock_integrating_physbio_2020,
AUTHOR = {K. Johnson and G. Howard and D. Morgan and E. Brenner and
A. Gardner and R. Durrett and W. Mo and A. Al'Khafaji and E.D. Sontag and
A. Jarrett and T. Yankeelov and A. Brock},
JOURNAL = {Physical Biology},
TITLE = {Integrating transcriptomics and bulk time course data
into a mathematical framework to describe and predict therapeutic
resistance in cancer},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {016001},
VOLUME = {18},
KEYWORDS = {oncology, cancer, chemoresistance, resistance,
intratumor heterogeneity, population dynamics, DNA barcoding,
evolution, systems biology},
PDF = {../../FTPDIR/johnson_et_al_brock_published_plus_SI.pdf},
ABSTRACT = {The development of resistance to chemotherapy is a major
cause of treatment failure in cancer. Intratumoral heterogeneity and
phenotypic plasticity play a significant role in therapeutic
resistance. Individual cell measurements such as flow and mass
cytometry and single cell RNA sequencing (scRNA-seq) have been used
to capture and analyze this cell variability. In parallel,
longitudinal treatment-response data is routinely employed in order
to calibrate mechanistic mathematical models of heterogeneous
subpopulations of cancer cells viewed as compartments with
differential growth rates and drug sensitivities. This work combines
both approaches: single cell clonally-resolved transcriptome datasets
(scRNA-seq, tagging individual cells with unique barcodes that are
integrated into the genome and expressed as sgRNA's) and longitudinal
treatment response data, to fit a mechanistic mathematical model of
drug resistance dynamics for a MDA-MB-231 breast cancer cell line.
The explicit inclusion of the transcriptomic information in the
parameter estimation is critical for identification of the model
parameters and enables accurate prediction of new treatment regimens. }
}
@ARTICLE{sadeghi_greene_sontag_2020,
AUTHOR = {M. Sadeghi and J.M. Greene and E.D. Sontag},
JOURNAL = {Annual Reviews in Control},
TITLE = {Universal features of epidemic models under social
distancing guidelines},
YEAR = {2021},
OPTMONTH = {},
NOTE = {Also in bioRxiv, 2020, https://www.biorxiv.org/content/10.1101/2020.06.21.163931v2.},
OPTNUMBER = {},
PAGES = {426-440},
VOLUME = {51},
KEYWORDS = {epidemiology, COVID-19, COVID, systems biology},
URL = {https://www.sciencedirect.com/science/article/pii/S1367578821000237},
PDF = {../../FTPDIR/2020.06.21.163931v2.full.pdf},
ABSTRACT = {Different epidemiological models, from the classical SIR
system to more sophisticated ones involving population compartments
for socially distanced, quarantined, infection aware, asymptomatic
infected, and other individuals, share some remarkable dynamic
characteristics when contact rates are subject to periodic or
one-shot changes. In simple pulsed isolation policies, a linear
relationship is found among optimal start time and duration for
reduction of the infected peak. If a single interval social
distancing starts too early or too late it will be ineffective with
respect to decreasing the peak of infection. On the other hand, the
nonlinearity of epidemic models leads to non-monotone behavior of the
peak of infected population under periodic relaxation policies. This
observation led us to hypothesize that an additional single interval
social distancing at a proper time can significantly decrease the
infected peak of periodic policies, and we verified this improvement.},
DOI = {https://doi.org/10.1016/j.arcontrol.2021.04.004}
}
@ARTICLE{explicit_lockdowns_medrxiv_2021,
AUTHOR = {E.D. Sontag},
JOURNAL = {International Journal of Robust and Nonlinear Control, Special Issue on Control-Theoretic Approaches for Systems in the Life Sciences},
TITLE = {An explicit formula for minimizing the infected peak in
an SIR epidemic model when using a fixed number of complete lockdowns},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-24},
OPTVOLUME = {},
KEYWORDS = {epidemiology, COVID-19, COVID, systems biology,
epidemics},
PDF = {../../FTPDIR/2021_epidemics_perfect_lockdown_formula.pdf},
ABSTRACT = {Careful timing of NPIs (non-pharmaceutical
interventions) such as social distancing may avoid high ``second
waves'' of infections of COVID-19. This paper asks what should be the
timing of a set of K complete-lockdowns of prespecified lengths (such
as two weeks) so as to minimize the peak of the infective
compartment. Perhaps surprisingly, it is possible to give an explicit
and easily computable rule for when each lockdown should commence.
Simulations are used to show that the rule remains fairly accurate
even if lockdowns are not perfect.}
}
@ARTICLE{phong_et_membranes,
AUTHOR = {A.P. Tran and J.H. Meldon and E.D. Sontag},
JOURNAL = {Frontiers in Chemical Engineering},
TITLE = {Transient diffusion into a bi-layer membrane with mass
transfer resistance: Exact solution and time lag analysis},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {25},
VOLUME = {2},
KEYWORDS = {Bi-layer membrane, transient diffusion, heat conduction,
mass transfer resistance},
PDF = {../../FTPDIR/2021_01_tran_meldon_sontag_frontiers_chemical_engineering.pdf},
ABSTRACT = {Exact analytical and closed-form solutions to a problem
involving transient diffusion in a bi-layer membrane with external
transfer resistance are presented. In addition to the solutions of
the transient response, the lead and lag times that are often of
importance in the characterization of membranes and arise from the
analysis of the asymptotic behavior of the mass permeated through the
membrane are also provided. The solutions presented here are also
compared to previously derived limiting cases of the diffusion in a
bi-layer with an impermeable wall and constant concentrations at the
upstream and downstream boundaries. Analysis of the time lag shows
that this membrane property is independent of the direction of flow.
Finally, an outline is provided of how these solutions, which
characterize the response to a step function increase in
concentration, can be also used to derive more complex input
conditions. Adequately handling boundary layer effects has a wide
array of potential applications such as the study of bi-layer
undergoing phenomena of heat convection, gas film resistance, and
absorption/desorption.}
}
@ARTICLE{dushek2019,
AUTHOR = {N. Trendel and P. Kruger and S. Gaglione and J. Nguyen and
J. Pettmann and E.D. Sontag and O. Dushek},
JOURNAL = {Science Signaling},
TITLE = {Perfect adaptation of CD8+ T cell responses to constant
antigen input over a wide range of affinity is overcome by
costimulation},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {eaay9363},
VOLUME = {14},
KEYWORDS = {immunology, cell signaling, T cells, systems biology},
PDF = {../../FTPDIR/trendel_et_al_2021_science_signaling_perfect_adaptation_T_cells_including_SI.pdf},
ABSTRACT = {Maintaining and limiting T cell responses to constant
antigen stimulation is critical to control pathogens and maintain
self-tolerance, respectively. Antigen recognition by T cell receptors
(TCRs) induces signalling that activates T cells to produce cytokines
and also leads to the downregulation of surface TCRs. In other
systems, receptor downregulation can induce perfect adaptation to
constant stimulation by a mechanism known as state-dependent
inactivation that requires complete downregulation of the receptor or
the ligand. However, this is not the case for the TCR, and therefore,
precisely how TCR downregulation maintains or limits T cell responses
is controversial. Here, we observed that in vitro expanded primary
human T cells exhibit perfect adaptation in cytokine production to
constant antigen stimulation across a 100,000-fold variation in
affinity with partial TCR downregulation. By directly fitting a
mechanistic model to the data, we show that TCR downregulation
produces imperfect adaptation, but when coupled to a switch produces
perfect adaptation in cytokine production. A pre diction of the model
is that pMHC-induced TCR signalling continues after adaptation and
this is confirmed by showing that, while costimulation cannot prevent
adaptation, CD28 and 4-1BB signalling reactivated adapted T cells to
produce cytokines in a pMHC-dependent manner. We show that adaptation
also applied to 1st generation chimeric antigen receptor (CAR)-T
cells but is partially avoided in 2nd generation CARs. These findings
highlight that even partial TCR downregulation can limit T cell
responses by producing perfect adaptation rendering T cells dependent
on costimulation for sustained responses.}
}
@ARTICLE{williams-fizgerald_ivich_sontag_niedre2021_correspondence,
AUTHOR = {A.L. Williams and J.E. Fitzgerald and F. Ivich and
E.D. Sontag and M. Niedre},
JOURNAL = {npg Light: Science & Applications},
TITLE = {Comment on In vivo flow cytometry reveals a circadian
rhythm of circulating tumor cells},
YEAR = {2021},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {188},
VOLUME = {10},
KEYWORDS = {circulating tumor cells, liquid biopsy, cancer,
oncology, multiple myeloma, systems biology},
PDF = {../../FTPDIR/williams-fizgerald_ivich_sontag_niedre2021_correspondence.pdf},
ABSTRACT = {Correspondence regarding circulating tumor cell
detection}
}
@INPROCEEDINGS{21acc_miller__al_rfm_pools,
AUTHOR = {J. Miller and M.A. Al-Radhawi and E.D. Sontag},
BOOKTITLE = {Proc. 2021 Automatic Control Conference},
TITLE = {Mediating ribosomal competition by splitting pools},
YEAR = {2021},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1897-1902},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, synthetic biology, ribosomes, RFM,
ribosome flow model},
PDF = {../../FTPDIR/21acc_miller__al_rfm_pools.pdf},
ABSTRACT = {Conference version of paper published in IEEE Control
Systems Letters, 2020}
}
@INPROCEEDINGS{21acc_brancodeoliveira_siami_sontag,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
BOOKTITLE = {Proc. 2021 Automatic Control Conference},
TITLE = {Bilinear dynamical networks under malicious attack: an
efficient edge protection method},
YEAR = {2021},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1210-1216},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {Bilinear systems, adversarial attacks,
robustness measures, supermodular optimization},
PDF = {../../FTPDIR/21acc_brancodeoliveira_siami_sontag.pdf},
ABSTRACT = {In large-scale networks, agents and links are often
vulnerable to attacks. This paper focuses on continuous-time bilinear
networks, where additive disturbances model attacks or uncertainties
on agents/states (node disturbances), and multiplicative disturbances
model attacks or uncertainties on couplings between agents/states
(link disturbances). It investigates network robustness notion in
terms of the underlying digraph of the network, and structure of
exogenous uncertainties and attacks. Specifically, it defines a
robustness measure using the $\mathcal H_2$-norm of the network and
calculates it in terms of the reachability Gramian of the bilinear
system. The main result is that under certain conditions, the measure
is supermodular over the set of all possible attacked links. The
supermodular property facilitates the efficient solution finding of
the optimization problem. Examples illustrate how different
structures can make the system more or less vulnerable to malicious
attacks on links.}
}
@INPROCEEDINGS{21cdc_brancodeoliveira_siami_sontag,
AUTHOR = {de Oliveira, A.C.B and M. Siami and E.D. Sontag},
BOOKTITLE = {Proc. 2021 60th IEEE Conference on Decision and Control (CDC)},
TITLE = {Eminence in noisy bilinear networks},
YEAR = {2021},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4835-4840},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {Bilinear systems, H2 norm, centrality,
adversarial attacks, robustness measures},
PDF = {../../FTPDIR/21cdc_brancodeoliveira_siami_sontag.pdf},
ABSTRACT = {When measuring importance of nodes in a network, the
interconnections and dynamics are often supposed to be perfectly
known. In this paper, we consider networks of agents with both
uncertain couplings and dynamics. Network uncertainty is modeled by
structured additive stochastic disturbances on each agent's update
dynamics and coupling weights. We then study how these uncertainties
change the network's centralities. Disturbances on the couplings
between agents resul in bilinear dynamics, and classical centrality
indices from linear network theory need to be redefined. To do that,
we first show that, similarly to its linear counterpart, the squared
H2 norm of bilinear systems measures the trace of the steady-state
error covariance matrix subject to stochastic disturbances. This
makes the H2 norm a natural candidate for a performance metric of the
system. We propose a centrality index for the agents based on the H2
norm, and show how it depends on the network topology and the noise
structure. Finally, we simulate a few graphs to illustrate how
uncertainties on different couplings affect the agents' centrality
rankings compared to a linearized model of the same system.}
}
@INCOLLECTION{iss_encyclopedia_systems_control2019,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Encyclopedia of Systems and Control},
PUBLISHER = {Springer-Verlag},
TITLE = {Input-to-State Stability},
YEAR = {2020},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {J. Baillieul and T. Samad},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-9},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
input to output stability},
PDF = {../../FTPDIR/2020_sontag_iss_encyclopedia_systems_and_control.pdf},
ABSTRACT = {The notion of input to state stability (ISS)
qualitatively describes stability of the mapping from initial states
and inputs to internal states (and more generally outputs). This
encyclopedia-style article entry gives a brief introduction to the
definition of ISS and a discussion of equivalent characterizations.
It is an update of the article in the 2015 edition, including
additional citations to recent PDE work.}
}
@INCOLLECTION{fcd_encyclopedia_systems_control2019,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Encyclopedia of Systems and Control},
PUBLISHER = {Springer-Verlag},
TITLE = {Scale-invariance in biological sensing},
YEAR = {2020},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {J. Baillieul and T. Samad},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-4},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
fold-change detection},
PDF = {../../FTPDIR/2020_sontag_scale_invariance_encyclopedia.pdf},
ABSTRACT = {The phenomenon of fold-change detection, or
scale-invariance, is exhibited by a variety of sensory systems, in
both bacterial and eukaryotic signaling pathways. This
encyclopedia-style article gives a brief introduction to the subject.},
DOI = {10.1007/978-1-4471-5102-9_100090-1}
}
@ARTICLE{2019_agrawal_khare_sontag_theory_enzyme_circuits,
AUTHOR = {D.K. Agrawal and E.M. Dolan and N.E. Hernandez and
K.M. Blacklock and S.D. Khare and E.D. Sontag},
JOURNAL = {ACS Synthetic Biology},
TITLE = {Mathematical models of protease-based enzymatic
biosensors},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {198-208},
VOLUME = {9},
KEYWORDS = {synthetic biology, protease-based circuits,
enzymatic circuits, systems biology, Boolean circuits},
PDF = {../../FTPDIR/agrawal_dolan_hernandez_blacklock_khare_sontag_protease_circuits_acs_2020.pdf},
ABSTRACT = {An important goal of synthetic biology is to build
biosensors and circuits with well-defined input-output relationships
that operate at speeds found in natural biological systems. However,
for molecular computation, most commonly used genetic circuit
elements typically involve several steps from input detection to
output signal production: transcription, translation, and
post-translational modifications. These multiple steps together
require up to several hours to respond to a single stimulus, and this
limits the overall speed and complexity of genetic circuits. To
address this gap, molecular frameworks that rely exclusively on
post-translational steps to realize reaction networks that can
process inputs at a time scale of seconds to minutes have been
proposed. Here, we build mathematical models of fast biosensors
capable of producing Boolean logic functionality. We employ
protease-based chemical and light-induced switches, investigate their
operation, and provide selection guidelines for their use as on-off
switches. As a proof of concept, we implement a rapamycin-induced
switch in vitro and demonstrate that its response qualitatively
agrees with the predictions from our models. We then use these
switches as elementary blocks, developing models for biosensors that
can perform OR and XOR Boolean logic computation while using reaction
conditions as tuning parameters. We use sensitivity analysis to
determine the time-dependent sensitivity of the output to proteolytic
and protein-protein binding reaction parameters. These fast
protease-based biosensors can be used to implement complex molecular
circuits with a capability of processing multiple inputs controllably
and algorithmically. Our framework for evaluating and optimizing
circuit performance can be applied to other molecular logic circuits.}
}
@ARTICLE{2019_alradhawi_angeli_sontag_lyapunov,
AUTHOR = {M.A. Al-Radhawi and D. Angeli and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {A computational framework for a Lyapunov-enabled
analysis of biochemical reaction networks},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {16(2): e1007681},
OPTVOLUME = {},
KEYWORDS = {MAPK cascades, Lyapunov functions, stability,
chemical networks, chemical rection networks, systems biology, RFM,
ribosome flow model},
PDF = {../../FTPDIR/mali_alradhawi_angeli_sontag_lyapunov_crn_plos2020.pdf},
ABSTRACT = {This paper deals with the analysis of the dynamics of
chemical reaction networks, developing a theoretical framework based
only on graphical knowledge and applying regardless of the particular
form of kinetics. This paper introduces a class of networks that are
"structurally (mono) attractive", by which we mean that they are
incapable of exhibiting multiple steady states, oscillation, or chaos
by the virtue of their reaction graphs. These networks are
characterized by the existence of a universal energy-like function
which we call a Robust Lyapunov function (RLF). To find such
functions, a finite set of rank-one linear systems is introduced,
which form the extremals of a linear convex cone. The problem is then
reduced to that of finding a common Lyapunov function for this set of
extremals. Based on this characterization, a computational package,
Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided
that constructs such functions or rules out their existence. An
extensive study of biochemical networks demonstrates that LEARN
offers a new unified framework. We study basic motifs, three-body
binding, and transcriptional networks. We focus on cellular
signalling networks including various post-translational modification
cascades, phosphotransfer and phosphorelay networks, T-cell kinetic
proofreading, ERK signaling, and the Ribosome Flow Model.}
}
@ARTICLE{boolean_distributed_april2020,
AUTHOR = {M.A. Al-Radhawi and A.P. Tran and E. Ernst and T. Chen and
C.A. Voigt and E.D. Sontag},
JOURNAL = {ACS Synthetic Biology},
TITLE = {Distributed implementation of Boolean functions by
transcriptional synthetic circuits},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2172-2187},
VOLUME = {9},
KEYWORDS = {synthetic biology, transcriptional networks,
gene networks, boolean circuits, boolean gates, systems biology},
PDF = {../../FTPDIR/mali_alradhawi_tran_erst_chen_voigt_sontag_boolean_distributed_acs_synbio_2020.pdf},
ABSTRACT = {Starting in the early 2000s, sophisticated technologies
have been developed for the rational construction of synthetic
genetic networks that implement specified logical functionalities.
Despite impressive progress, however, the scaling necessary in order
to achieve greater computational power has been hampered by many
constraints, including repressor toxicity and the lack of large sets
of mutually-orthogonal repressors. As a consequence, a typical
circuit contains no more than roughly seven repressor-based gates per
cell. A possible way around this scalability problem is to distribute
the computation among multiple cell types, which communicate among
themselves using diffusible small molecules (DSMs) and each of which
implements a small sub-circuit. Examples of DSMs are those employed
by quorum sensing systems in bacteria. This paper focuses on
systematic ways to implement this distributed approach, in the
context of the evaluation of arbitrary Boolean functions. The unique
characteristics of genetic circuits and the properties of DSMs
require the development of new Boolean synthesis methods, distinct
from those classically used in electronic circuit design. In this
work, we propose a fast algorithm to synthesize distributed
realizations for any Boolean function, under constraints on the
number of gates per cell and the number of orthogonal DSMs. The
method is based on an exact synthesis algorithm to find the minimal
circuit per cell, which in turn allows us to build an extensive
database of Boolean functions up to a given number of inputs. For
concreteness, we will specifically focus on circuits of up to 4
inputs, which might represent, for example, two chemical inducers and
two light inputs at different frequencies. Our method shows that,
with a constraint of no more than seven gates per cell, the use of a
single DSM increases the total number of realizable circuits by at
least 7.58-fold compared to centralized computation. Moreover, when
allowing two DSM's, one can realize 99.995\% of all possible 4-input
Boolean functions, still with at most 7 gates per cell. The
methodology introduced here can be readily adapted to complement
recent genetic circuit design automation software.},
DOI = {10.1021/acssynbio.0c00228}
}
@ARTICLE{chen_et_al_2020,
AUTHOR = {T. Chen and M.A. Al-Radhawi and E.D. Sontag},
JOURNAL = {Epigenetics},
TITLE = {A mathematical model exhibiting the effect of DNA
methylation on the stability boundary in cell-fate networks},
YEAR = {2020},
OPTMONTH = {},
NOTE = {PMID: 32842865},
OPTNUMBER = {},
PAGES = {1-22},
VOLUME = {15},
KEYWORDS = {methylation, differentiation, epigenetics,
pluripotent cells, gene regulatory networks, bistability,
bistability, systems biology},
PDF = {../../FTPDIR/chen_alradhawi_sontag_epigenetics_2020_with_SI.pdf},
ABSTRACT = {Cell-fate networks are traditionally studied within the
framework of gene regulatory networks. This paradigm considers only
interactions of genes through expressed transcription factors and
does not incorporate chromatin modification processes. This paper
introduces a mathematical model that seamlessly combines gene
regulatory networks and DNA methylation, with the goal of
quantitatively characterizing the contribution of epigenetic
regulation to gene silencing. The ``Basin of Attraction percentage''
is introduced as a metric to quantify gene silencing abilities. As a
case study, a computational and theoretical analysis is carried out
for a model of the pluripotent stem cell circuit as well as a
simplified self-activating gene model. The results confirm that the
methodology quantitatively captures the key role that methylation
plays in enhancing the stability of the silenced gene state.},
DOI = {10.1080/15592294.2020.1805686}
}
@ARTICLE{gevertz_greene_sanchez_sontag_JTB_covid_2020,
AUTHOR = {J.L. Gevertz and J.M. Greene and
Hixahuary Sanchez Tapia, C and E D Sontag},
JOURNAL = {Journal of Theoretical Biology},
TITLE = {A novel COVID-19 epidemiological model with explicit
susceptible and asymptomatic isolation compartments reveals
unexpected consequences of timing social distancing},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {110539},
VOLUME = {510},
KEYWORDS = {epidemiology, COVID-19, COVID, systems biology},
URL = {https://www.medrxiv.org/content/early/2020/05/18/2020.05.11.20098335},
PDF = {../../FTPDIR/2020_gevertz_greene_sancheztapia_sontag_jtb_covid_social_distancing.pdf},
ABSTRACT = {Motivated by the current COVID-19 epidemic, this work
introduces an epidemiological model in which separate compartments
are used for susceptible and asymptomatic "socially distant"
populations. Distancing directives are represented by rates of flow
into these compartments, as well as by a reduction in contacts that
lessens disease transmission. The dynamical behavior of this system
is analyzed, under various different rate control strategies, and the
sensitivity of the basic reproduction number to various parameters is
studied. One of the striking features of this model is the existence
of a critical implementation delay in issuing separation mandates:
while a delay of about four weeks does not have an appreciable
effect, issuing mandates after this critical time results in a far
greater incidence of infection. In other words, there is a nontrivial
but tight "window of opportunity" for commencing social distancing.
Different relaxation strategies are also simulated, with surprising
results. Periodic relaxation policies suggest a schedule which may
significantly inhibit peak infective load, but that this schedule is
very sensitive to parameter values and the schedule's frequency.
Further, we considered the impact of steadily reducing social
distancing measures over time. We find that a too-sudden reopening of
society may negate the progress achieved under initial distancing
guidelines, if not carefully designed.}
}
@ARTICLE{greene_sanchez_sontag_2020,
AUTHOR = {J. M. Greene and C. Sanchez-Tapia and E.D. Sontag},
JOURNAL = {Frontiers in Bioengineering and Biotechnology},
TITLE = {Mathematical details on a cancer resistance model},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {501: 1-27},
VOLUME = {8},
KEYWORDS = {resistance, chemotherapy, phenotype, optimal control,
singular controls, cancer, oncology, systems biology},
PDF = {../../FTPDIR/2020_greene_sancheztapia_sontag_frontiers_bioe.pdf},
ABSTRACT = {One of the most important factors limiting the success
of chemotherapy in cancer treatment is the phenomenon of drug
resistance. We have recently introduced a framework for quantifying
the effects of induced and non-induced resistance to cancer
chemotherapy. In this work, we expound on the details relating to an
optimal control problem outlined in our previous paper (Greene et
al., 2018). The control structure is precisely characterized as a
concatenation of bang-bang and path-constrained arcs via the
Pontryagin Maximum Principle and differential Lie algebraic
techniques. A structural identifiability analysis is also presented,
demonstrating that patient-specific parameters may be measured and
thus utilized in the design of optimal therapies prior to the
commencement of therapy. For completeness, a detailed analysis of
existence results is also included.},
DOI = {10.3389/fbioe.2020.00501}
}
@ARTICLE{special_issue_annual_reviews_epidemics1,
AUTHOR = {E. A. Hernandez-Vargas and G. Giordano and E.D. Sontag and
J. G. Chase and H. Chang and A. Astolfi},
JOURNAL = {Annual Reviews in Control},
TITLE = {First special section on systems and control research
efforts against COVID-19 and future pandemics},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {343-344},
VOLUME = {50},
KEYWORDS = {COVID-19, epidemiology, epidemics},
URL = {https://www.sciencedirect.com/science/article/pii/S1367578820300730},
DOI = {https://doi.org/10.1016/j.arcontrol.2020.10.007}
}
@ARTICLE{miller_et_al_rfm_pools,
AUTHOR = {J. Miller and M.A. Al-Radhawi and E.D. Sontag},
JOURNAL = {IEEE Control Systems Letters},
TITLE = {Mediating ribosomal competition by splitting pools},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1555-1560},
VOLUME = {5},
KEYWORDS = {systems biology, synthetic biology, ribosomes, RFM,
ribosome flow model},
PDF = {../../FTPDIR/2020_miller_alradhawi_sontag_ribosomes_ieee_control_letters.pdf},
ABSTRACT = {Synthetic biology constructs often rely upon the
introduction of "circuit" genes into host cells, in order to express
novel proteins and thus endow the host with a desired behavior. The
expression of these new genes "consumes" existing resources in the
cell, such as ATP, RNA polymerase, amino acids, and ribosomes.
Ribosomal competition among strands of mRNA may be described by a
system of nonlinear ODEs called the Ribosomal Flow Model (RFM). The
competition for resources between host and circuit genes can be
ameliorated by splitting the ribosome pool by use of orthogonal
ribosomes, where the circuit genes are exclusively translated by
mutated ribosomes. In this work, the RFM system is extended to
include orthogonal ribosome competition. This Orthogonal Ribosomal
Flow Model (ORFM) is proven to be stable through the use of Robust
Lyapunov Functions. The optimization problem of maximizing the
weighted protein translation rate by adjusting allocation of
ribosomal species is formulated and implemented. Note: publsihed Nov
2020, even though journal reprint says "Nov 2021".}
}
@ARTICLE{bell_shaped_no_iffl_biorxiv2020,
AUTHOR = {E.D. Sontag},
JOURNAL = {bioRxiv},
TITLE = {Bell-shaped dose response for a system with no IFFLs},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTVOLUME = {},
KEYWORDS = {IFFL, feedforward loops, nonlinear systems, immunology},
PUBLISHER = {Cold Spring Harbor Laboratory},
PDF = {https://www.biorxiv.org/content/10.1101/2020.11.17.387605v3},
ABSTRACT = {It is well known that the presence of an incoherent
feedforward loop (IFFL) in a network may give rise to a steady state
non-monotonic dose response. This note shows that the converse
implication does not hold. It gives an example of a three-dimensional
system that has no IFFLs, yet its dose response is bell-shaped. It
also studies under what conditions the result is true for
two-dimensional systems, in the process recovering, in far more
generality, a result given in the T-cell activation literature.}
}
@ARTICLE{2019_phong_tran1,
AUTHOR = {A.P. Tran and M.A. Al-Radhawi and I. Kareva and J. Wu and
D.J. Waxman and E.D. Sontag},
JOURNAL = {Frontiers in Immunology},
TITLE = {Delicate balances in cancer chemotherapy: Modeling
immune recruitment and emergence of systemic drug resistance},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1376-},
VOLUME = {11},
KEYWORDS = {metronomic chemotherapy, cyclophosphamide,
mathematical modeling, immune recruitment, cancer, resistance,
oncology, immunology, systems biology},
PDF = {../../FTPDIR/2020_tran_et_al_metronomic_model_frontiers_immunology.pdf},
ABSTRACT = {Metronomic chemotherapy can drastically enhance
immunogenic tumor cell death. However, the responsible mechanisms are
still incompletely understood. Here, we develop a mathematical model
to elucidate the underlying complex interactions between tumor
growth, immune system activation, and therapy-mediated immunogenic
cell death. Our model is conceptually simple, yet it provides a
surprisingly excellent fit to empirical data obtained from a GL261
mouse glioma model treated with cyclophosphamide on a metronomic
schedule. The model includes terms representing immune recruitment as
well as the emergence of drug resistance during prolonged metronomic
treatments. Strikingly, a fixed set of parameters, not adjusted for
individuals nor for drug schedule, excellently recapitulates
experimental data across various drug regimens, including treatments
administered at intervals ranging from 6 to 12 days. Additionally,
the model predicts peak immune activation times, rediscovering
experimental data that had not been used in parameter fitting or in
model construction. The validated model was then used to make
predictions about expected tumor-immune dynamics for novel drug
administration schedules. Notably, the validated model suggests that
immunostimulatory and immunosuppressive intermediates are responsible
for the observed phenomena of resistance and immune cell recruitment,
and thus for variation of responses with respect to different
schedules of drug administration.},
DOI = {10.3389/fimmu.2020.01376}
}
@ARTICLE{williams-fizgerald_ivich_sontag_niedre2020,
AUTHOR = {A.L. Williams and J.E. Fitzgerald and F. Ivich and
E.D. Sontag and M. Niedre},
JOURNAL = {Frontiers in Oncology},
TITLE = {Short-term circulating tumor cell dynamics in mouse
xenograft models and implications for liquid biopsy},
YEAR = {2020},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2447-},
VOLUME = {10},
KEYWORDS = {circulating tumor cells, liquid biopsy, cancer,
oncology, multiple myeloma, systems biology},
PDF = {../../FTPDIR/2020_frontiers_oncology_williams_et_al_niedre_with_SI.pdf},
ABSTRACT = {Circulating tumor cells (CTCs) are widely studied using
liquid biopsy methods that analyze single, fractionally-small
peripheral blood (PB) samples. However, little is known about
fluctuations in CTC numbers that occur over short timescales in vivo,
and how these may affect accurate enumeration from blood samples.
Diffuse in vivo flow cytometry (DiFC) developed by the Niedre lab
allows continuous, non-invasive counting of rare, green fluorescent
protein expressing CTCs in large deeply-seated blood vessels in mice.
Here, DiFC is used to study short-term changes in CTC numbers in
multiple myeloma and Lewis lung carcinoma xenograft models. Both 35-
to 50-minute data sets are analyzed, with intervals corresponding to
approximately 1, 5, 10 and 20\% of the PB volume, as well as changes
over 24-hour periods. For rare CTCs, the use of short DiFC intervals
(corresponding to small PB samples) frequently resulted in no
detections. For more abundant CTCs, CTC numbers frequently varied by
an order of magnitude or more over the time-scales considered. This
variability far exceeded that expected by Poisson statistics, and
instead was consistent with rapidly changing mean numbers of CTCs in
the PB. Because of these natural temporal changes, accurately
enumerating CTCs from fractionally small blood samples is inherently
problematic. The problem is likely to be compounded for multicellular
CTC clusters or specific CTC subtypes. However, it is also shown that
enumeration can be improved by averaging multiple samples, analysis
of larger volumes, or development of new methods for enumeration of
CTCs directly in vivo.},
DOI = {10.3389/fonc.2020.601085}
}
@ARTICLE{2019_deepak_integral_controller,
AUTHOR = {D.K. Agrawal and R. Marshall and V. Noireaux and
E.D. Sontag},
JOURNAL = {Nature Communications},
TITLE = {In vitro implementation of robust gene regulation in a
synthetic biomolecular integral controller},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-12},
VOLUME = {10},
KEYWORDS = {tracking, synthetic biology, integral feedback, TX/TL,
systems biology, dynamical systems, adaptation,
internal model principle, identifiability},
PDF = {../../FTPDIR/agrawal_marshall_noireaux_sontag_natcom_with_SI.pdf},
ABSTRACT = {Cells respond to biochemical and physical internal as
well as external signals. These signals can be broadly classified
into two categories: (a) ``actionable'' or ``reference'' inputs that
should elicit appropriate biological or physical responses such as
gene expression or motility, and (b) ``disturbances'' or
``perturbations'' that should be ignored or actively filtered-out.
These disturbances might be exogenous, such as binding of nonspecific
ligands, or endogenous, such as variations in enzyme concentrations
or gene copy numbers. In this context, the term robustness describes
the capability to produce appropriate responses to reference inputs
while at the same time being insensitive to disturbances. These two
objectives often conflict with each other and require delicate design
trade-offs. Indeed, natural biological systems use complicated and
still poorly understood control strategies in order to finely balance
the goals of responsiveness and robustness. A better understanding of
such natural strategies remains an important scientific goal in
itself and will play a role in the construction of synthetic circuits
for therapeutic and biosensing applications. A prototype problem in
robustly responding to inputs is that of ``robust tracking'', defined
by the requirement that some designated internal quantity (for
example, the level of expression of a reporter protein) should
faithfully follow an input signal while being insensitive to an
appropriate class of perturbations. Control theory predicts that a
certain type of motif, called integral feedback, will help achieve
this goal, and this motif is, in fact, a necessary feature of any
system that exhibits robust tracking. Indeed, integral feedback has
always been a key component of electrical and mechanical control
systems, at least since the 18th century when James Watt employed the
centrifugal governor to regulate steam engines. Motivated by this
knowledge, biological engineers have proposed various designs for
biomolecular integral feedback control mechanisms. However, practical
and quantitatively predictable implementations have proved
challenging, in part due to the difficulty in obtaining accurate
models of transcription, translation, and resource competition in
living cells, and the stochasticity inherent in cellular reactions.
These challenges prevent first-principles rational design and
parameter optimization. In this work, we exploit the versatility of
an Escherichia coli cell-free transcription-translation (TXTL) to
accurately design, model and then build, a synthetic biomolecular
integral controller that precisely controls the expression of a
target gene. To our knowledge, this is the first design of a
functioning gene network that achieves the goal of making gene
expression track an externally imposed reference level, achieves this
goal even in the presence of disturbances, and whose performance
quantitatively agrees with mathematical predictions.}
}
@ARTICLE{mali_delvecchio_sontag_slow_gene_binding_2017,
AUTHOR = {M. A. Al-Radhawi and Del Vecchio, D. and E. D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Multi-modality in gene regulatory networks with slow
gene binding},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1006784},
VOLUME = {15},
KEYWORDS = {multistability, gene networks, Markov Chains,
Master Equation, cancer heterogeneity, phenotypic variation,
nonlinear systems, stochastic systems, epigenetics,
chemical master equations, systems biology},
PDF = {https://doi.org/10.1371/journal.pcbi.1006784},
ABSTRACT = {In biological processes such as embryonic development,
hematopoietic cell differentiation, and the arising of tumor
heterogeneity and consequent resistance to therapy, mechanisms of
gene activation and deactivation may play a role in the emergence of
phenotypically heterogeneous yet genetically identical (clonal)
cellular populations. Mathematically, the variability in phenotypes
in the absence of genetic variation can be modeled through the
existence of multiple metastable attractors in nonlinear systems
subject with stochastic switching, each one of them associated to an
alternative epigenetic state. An important theoretical and practical
question is that of estimating the number and location of these
states, as well as their relative probabilities of occurrence. This
paper focuses on a rigorous analytic characterization of multiple
modes under slow promoter kinetics, which is a feature of epigenetic
regulation. It characterizes the stationary distributions of Chemical
Master Equations for gene regulatory networks as a mixture of Poisson
distributions. As illustrations, the theory is used to tease out the
role of cooperative binding in stochastic models in comparison to
deterministic models, and applications are given to various model
systems, such as toggle switches in isolation or in communicating
populations and a trans-differentiation network.}
}
@ARTICLE{greene_gevertz_sontag_resistance_2017,
AUTHOR = {J.M. Greene and J.L. Gevertz and E. D. Sontag},
JOURNAL = {JCO Clinical Cancer Informatics},
TITLE = {A mathematical approach to distinguish spontaneous from
induced evolution of drug resistance during cancer treatment},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-20},
VOLUME = {DOI: 10.1200/CCI.18.00087},
KEYWORDS = {cancer heterogeneity, phenotypic variation,
nonlinear systems, epigenetics, oncology, cancer, systems biology},
PDF = {../../FTPDIR/2019_greene_gevertz_sontag_asco.pdf},
ABSTRACT = {Resistance to chemotherapy is a major impediment to the
successful treatment of cancer. Classically, resistance has been
thought to arise primarily through random genetic mutations, after
which mutated cells expand via Darwinian selection. However, recent
experimental evidence suggests that the progression to resistance
need not occur randomly, but instead may be induced by the
therapeutic agent itself. This process of resistance induction can be
a result of genetic changes, or can occur through epigenetic
alterations that cause otherwise drug-sensitive cancer cells to
undergo "phenotype switching". This relatively novel notion of
resistance further complicates the already challenging task of
designing treatment protocols that minimize the risk of evolving
resistance. In an effort to better understand treatment resistance,
we have developed a mathematical modeling framework that incorporates
both random and drug-induced resistance. Our model demonstrates that
the ability (or lack thereof) of a drug to induce resistance can
result in qualitatively different responses to the same drug dose and
delivery schedule. The importance of induced resistance in treatment
response led us to ask if, in our model, one can determine the
resistance induction rate of a drug for a given treatment protocol.
Not only could we prove that the induction parameter in our model is
theoretically identifiable, we have also proposed a possible in vitro
experiment which could practically be used to determine a treatment's
propensity to induce resistance.}
}
@ARTICLE{margaliot_sontag_tridiagonal_automatica2018,
AUTHOR = {M. Margaliot and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Revisiting totally positive differential systems: A
tutorial and new results},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-14},
VOLUME = {101},
KEYWORDS = {tridiagonal systems, cooperative systems,
monotone systems},
PDF = {../../FTPDIR/margaliot_sontag_totally_positive_automatica2019.pdf},
ABSTRACT = {A matrix is totally nonnegative (resp., totally
positive) if all its minors are nonnegative (resp., positive). This
paper draws connections between B. Schwarz's 1970 work on TN and TP
matrices to Smillie's 1984 and Smith's 1991 work on stability of
nonlinear tridiagonal cooperative systems, simplifying proofs in the
later paper and suggesting new research questions.}
}
@ARTICLE{nikolaev_zloza_sontag_2018,
AUTHOR = {E.V. Nikolaev and A. Zloza and E.D. Sontag},
JOURNAL = {Frontiers in Immunology},
TITLE = {Immunobiochemical reconstruction of influenza lung
infection - melanoma skin cancer interactions},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {Article 4},
VOLUME = {10},
KEYWORDS = {oncology, cancer, infections, immunology,
checkpoint inhibition, systems biology},
PDF = {../../FTPDIR/2019_01_nikolaev_zloza_sontag_frontiers_immunology_melanoma_flu.pdf},
ABSTRACT = {Recent experimental results from the Zloza lab combined
a mouse model of influenza A virus (IAV) infection (A/H1N1/PR8) and a
highly aggressive model of infection-unrelated cancer, B16-F10 skin
melanoma. This paper showed that acute influenza infection of the
lung promotes distal melanoma growth in the dermis of the flank and
leads to decreased host survival. Here, we proceed to ground the
experimental observations in a mechanistic immunobiochemical model
that incorporates the T cell receptor signaling pathway, various
transcription factors, and a gene regulatory network (GRN). A core
component of our model is a biochemical motif, which we call a Triple
Incoherent Feed-Forward Loop (TIFFL), and which reflects known
interactions between IRF4, Blimp-1, and Bcl-6. The different activity
levels of the TIFFL components, as a function of the cognate antigen
levels and the given inflammation context, manifest themselves in
phenotypically distinct outcomes. Specifically, both the TIFFL
reconstruction and quantitative estimates obtained from the model
allowed us to formulate a hypothesis that it is the loss of the
fundamental TIFFL-induced adaptation of the expression of PD-1
receptors on anti-melanoma CD8+ T cells that constitutes the essence
of the previously unrecognized immunologic factor that promotes the
experimentally observed distal tumor growth in the presence of acute
non-ocogenic infection. We therefore hope that this work can further
highlight the importance of adaptive mechanisms by which immune
functions contribute to the balance between self and non-self immune
tolerance, adaptive resistance, and the strength of TCR-induced
activation, thus contributing to the understanding of a broader
complexity of fundamental interactions between pathogens and tumors.}
}
@ARTICLE{2019_css_letters_congestion,
AUTHOR = {M. Sadeghi and M.A. Al-Radhawi and M. Margaliot and
E.D. Sontag},
JOURNAL = {IEEE Control Systems Letters},
TITLE = {No switching policy is optimal for a positive linear
system with a bottleneck entrance},
YEAR = {2019},
OPTMONTH = {},
NOTE = {(Also in Proc. 2019 IEEE Conf. Decision and Control.)},
OPTNUMBER = {},
PAGES = {889-894},
VOLUME = {3},
KEYWORDS = {entrainment, switched systems, RFM, ribosome flow model,
traffic systems, nonlinear systems, nonlinear control},
PDF = {../../FTPDIR/2019_sadeghi_al-radhawi_margaliot_sontag_bottleneck_ieee_css_letters.pdf},
ABSTRACT = {We consider a nonlinear SISO system that is a cascade of
a scalar "bottleneck entrance" with a stable positive linear system.
In response to any periodic inflow, all solutions converge to a
unique periodic solution with the same period. We study the problem
of maximizing the averaged throughput via controlled switching. We
compare two strategies: 1) switching between a high and low value,
and 2 ~using a constant inflow equal to the prescribed mean value. We
show that no possible switching policy can outperform a constant
inflow rate, though it can approach it asymptotically. We describe
several potential applications of this problem in traffic systems,
ribosome flow models, and scheduling at security checks.}
}
@ARTICLE{wang_lin_sontag_sorger2019,
AUTHOR = {S. Wang and J.-R. Lin and E.D. Sontag and P.K. Sorger},
JOURNAL = {PLoS Computational Biology},
TITLE = {Inferring reaction network structure from single-cell,
multiplex data, using toric systems theory},
YEAR = {2019},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1007311},
VOLUME = {15},
KEYWORDS = {reaction networks, reaction networks, stoichiometry,
complex balancing, toric varieties, systems biology},
URL = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007311},
PDF = {../../FTPDIR/wang_lin_sontag_sorger_plos2020.pdf},
ABSTRACT = {The goal of many single-cell studies on eukaryotic cells
is to gain insight into the biochemical reactions that control cell
fate and state. This paper introduces the concept of effective
stoichiometric space (ESS) to guide the reconstruction of biochemical
networks from multiplexed, fixed time-point, single-cell data. In
contrast to methods based solely on statistical models of data, the
ESS method leverages the power of the geometric theory of toric
varieties to begin unraveling the structure of chemical reaction
networks (CRN). This application of toric theory enables a
data-driven mapping of covariance relationships in single cell
measurements into stoichiometric information, one in which each cell
subpopulation has its associated ESS interpreted in terms of CRN
theory. In the development of ESS we reframe certain aspects of the
theory of CRN to better match data analysis. As an application of our
approach we process cytomery- and image-based single-cell datasets
and identify differences in cells treated with kinase inhibitors. Our
approach is directly applicable to data acquired using readily
accessible experimental methods such as Fluorescence Activated Cell
Sorting (FACS) and multiplex immunofluorescence.}
}
@INPROCEEDINGS{19cdc_sequestration,
AUTHOR = {D. K. Agrawal and R. Marshall and M.A. Al-Radhawi and
V. Noireaux and E. D. Sontag},
BOOKTITLE = {Proc. 2019 IEEE Conf. Decision and Control},
TITLE = {Some remarks on robust gene regulation in a biomolecular
integral controller},
YEAR = {2019},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2820-2825},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
tracking, synthetic biology, integral feedback, TX/TL,
systems biology, dynamical systems, adaptation,
internal model principle, systems biology},
PDF = {../../FTPDIR/2019_cdc_integral_controller.pdf},
ABSTRACT = {Integral feedback can help achieve robust tracking
independently of external disturbances. Motivated by this knowledge,
biological engineers have proposed various designs of biomolecular
integral feedback controllers to regulate biological processes. In
this paper, we theoretically analyze the operation of a particular
synthetic biomolecular integral controller, which we have recently
proposed and implemented experimentally. Using a combination of
methods, ranging from linearized analysis to sum-of-squares (SOS)
Lyapunov functions, we demonstrate that, when the controller is
operated in closed-loop, it is capable of providing integral
corrections to the concentration of an output species in such a
manner that the output tracks a reference signal linearly over a
large dynamic range. We investigate the output dependency on the
reaction parameters through sensitivity analysis, and quantify
performance using control theory metrics to characterize response
properties, thus providing clear selection guidelines for practical
applications. We then demonstrate the stable operation of the
closed-loop control system by constructing quartic Lyapunov functions
using SOS optimization techniques, and establish global stability for
a unique equilibrium. Our analysis suggests that by incorporating
effective molecular sequestration, a biomolecular closed-loop
integral controller that is capable of robustly regulating gene
expression is feasible.}
}
@INPROCEEDINGS{19acc,
AUTHOR = {S. Bruno and M.A. Al-Radhawi and E.D. Sontag and
Del Vecchio, D.},
BOOKTITLE = {Proc. 2019 Automatic Control Conference},
TITLE = {Stochastic analysis of genetic feedback controllers to
reprogram a pluripotency gene regulatory network},
YEAR = {2019},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5089-5096},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {multistability, reaction networks, systems biology,
stochastic systems, cell differentiation, multistationarity,
chemical master equations},
PDF = {../../FTPDIR/2019_acc_stochastic_pluripotency_bruno_alradhawi_sontag_delvecchio_reprint.pdf},
ABSTRACT = {Cellular reprogramming is traditionally accomplished
through an open loop control approach, wherein key transcription
factors are injected in cells to steer a gene regulatory network
toward a pluripotent state. Recently, a closed loop feedback control
strategy was proposed in order to achieve more accurate control.
Previous analyses of the controller were based on deterministic
models, ignoring the substantial stochasticity in these networks,
Here we analyze the Chemical Master Equation for reaction models with
and without the feedback controller. We computationally and
analytically investigate the performance of the controller in
biologically relevant parameter regimes where stochastic effects
dictate system dynamics. Our results indicate that the feedback
control approach still ensures reprogramming even when analyzed using
a stochastic model.}
}
@TECHREPORT{chen_et_al_biorxiv2019,
AUTHOR = {T. Chen and M. A. Al-Radhawi and E. D. Sontag},
INSTITUTION = {Cold Spring Harbor Laboratory},
TITLE = {A mathematical model exhibiting the effect of DNA
methylation on the stability boundary in cell-fate networks},
YEAR = {2019},
OPTADDRESS = {},
OPTMONTH = {},
NOTE = {BioRxiv preprint 10.1101/2019.12.19.883280},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {Cell-fate networks, gene regulatory networks,
DNA methylation, epigenetic regulation,
pluripotent stem cell circuit},
ABSTRACT = {Cell-fate networks are traditionally studied within the
framework of gene regulatory networks. This paradigm considers only
interactions of genes through expressed transcription factors and
does not incorporate chromatin modification processes. This paper
introduces a mathematical model that seamlessly combines gene
regulatory networks and DNA methylation, with the goal of
quantitatively characterizing the contribution of epigenetic
regulation to gene silencing. The ``Basin of Attraction percentage''
is introduced as a metric to quantify gene silencing abilities. As a
case study, a computational and theoretical analysis is carried out
for a model of the pluripotent stem cell circuit as well as a
simplified self-activating gene model. The results confirm that the
methodology quantitatively captures the key role that methylation
plays in enhancing the stability of the silenced gene state.}
}
@TECHREPORT{gevertz_greene_sontag_biorxiv2019,
AUTHOR = {J.L. Gevertz and J.M. Greene and E.D. Sontag},
INSTITUTION = {Cold Spring Harbor Laboratory},
TITLE = {Validation of a mathematical model of cancer
incorporating spontaneous and induced evolution to drug resistance},
YEAR = {2019},
OPTADDRESS = {},
OPTMONTH = {},
NOTE = {BioRxiv preprint 10.1101/2019.12.27.889444},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {cancer heterogeneity, phenotypic variation,
nonlinear systems, epigenetics, optimal control theory, oncology,
cancer},
ABSTRACT = {This paper continues the study of a model which was
introduced in earlier work by the authors to study spontaneous and
induced evolution to drug resistance under chemotherapy. The model is
fit to existing experimental data, and is then validated on
additional data that had not been used when fitting. In addition, an
optimal control problem is studied numerically.}
}
@TECHREPORT{arxiv_margaliot_sontag_antithetic_dec2019,
AUTHOR = {M. Margaliot and E.D. Sontag},
INSTITUTION = {bioRxiv 2019/868000v1},
TITLE = {Compact attractors of an antithetic integral feedback
system have a simple structure},
YEAR = {2019},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {Poincare-Bendixson, k-cooperative dynamical systems,
sign-regular matrices, synthetic biology, antithetic feedback},
PDF = {https://www.biorxiv.org/content/10.1101/868000v1},
ABSTRACT = {Since its introduction by Briat, Gupta and Khammash, the
antithetic feedback controller design has attracted considerable
attention in both theoretical and experimental systems biology. The
case in which the plant is a two-dimensional linear system (making
the closed-loop system a nonlinear four-dimensional system) has been
analyzed in much detail. This system has a unique equilibrium but,
depending on parameters, it may exhibit periodic orbits. This note
shows that, for any parameter choices, every bounded trajectory
satisfies a Poincare'-Bendixson property: the dynamics in the
omega-limit set of any precompact solution is conjugate to the
dynamics in a compact invariant subset of a two-dimensional Lipschitz
dynamical system, thus precluding chaotic and other strange
attractors. }
}
@TECHREPORT{tran_et_al_biorxiv2019,
AUTHOR = {A. P. Tran and M. A. Al-Radhawi and I. Kareva and J. Wu and
D. J. Waxman and E. D. Sontag},
INSTITUTION = {Cold Spring Harbor Laboratory},
TITLE = {Delicate balances in cancer chemotherapy: modeling
immune recruitment and emergence of systemic drug resistance},
YEAR = {2019},
OPTADDRESS = {},
OPTMONTH = {},
NOTE = {bioRxiv 2019.12.12.874891},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {chemotherapy, immunology, immune system, oncology,
cancer, metronomic},
ABSTRACT = {Metronomic chemotherapy can drastically enhance
immunogenic tumor cell death. However, the responsible mechanisms are
still incompletely understood. Here, we develop a mathematical model
to elucidate the underlying complex interactions between tumor
growth, immune system activation, and therapy-mediated immunogenic
cell death. Our model is conceptually simple, yet it provides a
surprisingly excellent fit to empirical data obtained from a GL261
mouse glioma model treated with cyclophosphamide on a metronomic
schedule. The model includes terms representing immune recruitment as
well as the emergence of drug resistance during prolonged metronomic
treatments. Strikingly, a fixed set of parameters, not adjusted for
individuals nor for drug schedule, excellently recapitulates
experimental data across various drug regimens, including treatments
administered at intervals ranging from 6 to 12 days. Additionally,
the model predicts peak immune activation times, rediscovering
experimental data that had not been used in parameter fitting or in
model construction. The validated model was then used to make
predictions about expected tumor-immune dynamics for novel drug
administration schedules. Notably, the validated model suggests that
immunostimulatory and immunosuppressive intermediates are responsible
for the observed phenomena of resistance and immune cell recruitment,
and thus for variation of responses with respect to different
schedules of drug administration.}
}
@INCOLLECTION{2018_moments_sagar_book,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Emerging Applications of Control and Systems Theory},
PUBLISHER = {Springer-Verlag},
TITLE = {Examples of computation of exact moment dynamics for
chemical reaction networks},
YEAR = {2018},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {R. Tempo and S. Yurkovich and P. Misra},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {295-312},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {473},
KEYWORDS = {chemical master equations, stochastic systems, moments,
reaction networks, reaction networks, incoherent feedforward loop,
feedforward, IFFL, systems biology},
PDF = {../../FTPDIR/2018_moments_sagar_book.pdf},
ABSTRACT = {The study of stochastic biomolecular networks is a key
part of systems biology, as such networks play a central role in
engineered synthetic biology constructs as well as in naturally
occurring cells. This expository paper reviews in a unified way a
pair of recent approaches to the finite computation of statistics for
chemical reaction networks.}
}
@ARTICLE{delvecchio_qian_murray_sontag_annual_reviews2018,
AUTHOR = {Del Vecchio, D. and Y. Qian and R.M Murray and
E.D. Sontag},
JOURNAL = {Annual Reviews in Control},
TITLE = {Future systems and control research in synthetic biology},
YEAR = {2018},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {5-17},
VOLUME = {45},
KEYWORDS = {synthetic biology, systems biology},
PDF = {../../FTPDIR/delvecchio_qian_murray_sontag_annual_reviews_synthetic_biology_2018.pdf},
ABSTRACT = {This paper is a review of systems and control problems
in synthetic biology, focusing on past accomplishments and open
problems. It is partially a report on the workshop "The
Compositionality Problem in Synthetic Biology: New Directions for
Control Theory" held on June 26-27, 2017 at MIT, and organized by D.
Del Vecchio, R. M. Murray, and E. D. Sontag}
}
@ARTICLE{chaos2017,
AUTHOR = {E.V. Nikolaev and S.J. Rahi and E.D. Sontag},
JOURNAL = {Biophysical Journal},
TITLE = {Chaos in simple periodically-forced biological models},
YEAR = {2018},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1232-1240},
VOLUME = {114},
KEYWORDS = {chaos, entrainment, systems biology, periodic inputs,
subharmonic responses, biochemical systems, forced oscillations},
PDF = {../../FTPDIR/nikolaev_rahi_sontag_chaos_biophysical_journal_2018.pdf},
ABSTRACT = {What complicated dynamics can arise in the simplest
biochemical systems, in response to a periodic input? This paper
discusses two models that commonly appear as components of larger
sensing and signal transduction pathways in systems biology: a simple
two-species negative feedback loop, and a prototype nonlinear
integral feedback. These systems have globally attracting steady
states when unforced, yet, when subject to a periodic excitation,
subharmonic responses and strange attractors can arise via
period-doubling cascades. These behaviors are similar to those
exhibited by classical forced nonlinear oscillators such as those
described by van der Pol or Duffing equations. The lack of
entrainment to external oscillations, in even the simplest
biochemical networks, represents a level of additional complexity in
molecular biology.}
}
@ARTICLE{segall-shapiro2017,
AUTHOR = {T.H. Segall-Shapiro and E. D. Sontag and C. A. Voigt},
JOURNAL = {Nature Biotechnology},
TITLE = {Engineered promoters enable constant gene expression at
any copy number in bacteria},
YEAR = {2018},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {352-358},
VOLUME = {36},
KEYWORDS = {synthetic biology, systems biology, genetic circuits,
gene copy number, incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/segallshapiro_sontag_voigt_nat_methods_2018.pdf},
ABSTRACT = {This paper deals with the design of promoters that
maintain constant levels of expression, whether they are carried at
single copy in the genome or on high-copy plasmids. The design is
based on an incoherent feedforward loop (iFFL) with a perfectly
non-cooperative repression. The circuits are implemented in E. coli
using Transcription Activator Like Effectors (TALEs). The resulting
stabilized promoters generate near identical expression across
different genome locations and plasmid backbones (pSC101, p15a,
ColE1, pUC), and also provide robustness to strain mutations and
growth media. Further, their strength is tunable and can be used to
maintain constant ratios between proteins.}
}
@ARTICLE{zarai_margaliot_sontag_tuller_control_translation_2016,
AUTHOR = {Y. Zarai and M. Margaliot and E.D. Sontag and T. Tuller},
JOURNAL = {IEEE/ACM Transactions on Computational Biology and Bioinformatics},
TITLE = {Controllability analysis and control synthesis for the
ribosome flow model},
YEAR = {2018},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1351-1364},
VOLUME = {15},
KEYWORDS = {systems biology, ribosomes, controllability, RFM,
ribosome flow model},
PDF = {../../FTPDIR/zarai_margaliot_sontag_tuller_ieee_TCBB_july2018_rfm_controllability.pdf},
ABSTRACT = {The ribosomal density along the coding region of the
mRNA molecule affects various fundamental intracellular phenomena
including: protein production rates, organismal fitness, ribosomal
drop off, and co-translational protein folding. Thus, regulating
translation in order to obtain a desired ribosomal profile along the
mRNA molecule is an important biological problem. This paper studies
this problem formulated in the context of the ribosome flow model
(RFM) in which one views the transition rates between site as
controls.}
}
@INPROCEEDINGS{18cdc_mali,
AUTHOR = {M.A. Al-Radhawi and N.S. Kumar and E.D. Sontag and
Del Vecchio, D.},
BOOKTITLE = {Proc. 2018 IEEE Conf. Decision and Control},
TITLE = {Stochastic multistationarity in a model of the
hematopoietic stem cell differentiation network},
YEAR = {2018},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1886-1892},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {multistability, reaction networks, systems biology,
stochastic systems, cell differentiation, multistationarity,
chemical master equations},
PDF = {../../FTPDIR/mali_kumar_sontag_delvecchio_cdc2018.pdf},
ABSTRACT = {In the mathematical modeling of cell differentiation, it
is common to think of internal states of cells (quanfitied by
activation levels of certain genes) as determining different cell
types. We study here the "PU.1/GATA-1 circuit" that controls the
development of mature blood cells from hematopoietic stem cells
(HSCs). We introduce a rigorous chemical reaction network model of
the PU.1/GATA-1 circuit, which incorporates current biological
knowledge and find that the resulting ODE model of these biomolecular
reactions is incapable of exhibiting multistability, contradicting
the fact that differentiation networks have, by definition,
alternative stable steady states. When considering instead the
stochastic version of this chemical network, we analytically
construct the stationary distribution, and are able to show that this
distribution is indeed capable of admitting a multiplicity of modes.
Finally, we study how a judicious choice of system parameters serves
to bias the probabilities towards different stationary states. We
remark that certain changes in system parameters can be physically
implemented by a biological feedback mechanism; tuning this feedback
gives extra degrees of freedom that allow one to assign higher
likelihood to some cell types over others.}
}
@INPROCEEDINGS{18cdc_tutorial_control_biology,
AUTHOR = {F. Blanchini and H. El-Samad and G. Giordano and
E. D. Sontag},
BOOKTITLE = {Proc. 2018 IEEE Conf. Decision and Control},
TITLE = {Control-theoretic methods for biological networks},
YEAR = {2018},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {466-483},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, dynamic response phenotypes,
multistability, oscillations, feedback, nonlinear systems,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/blanchini-elsamad_giordano_sontag_cdc2018.pdf},
ABSTRACT = {This is a tutorial paper on control-theoretic methods
for the analysis of biological systems.}
}
@INPROCEEDINGS{18cdc_greene_sanchez,
AUTHOR = {J.M. Greene and C. Sanchez-Tapia and E.D. Sontag},
BOOKTITLE = {Proc. 2018 IEEE Conf. Decision and Control},
TITLE = {Control structures of drug resistance in cancer
chemotherapy},
YEAR = {2018},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5195-5200},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/greene_sanchez_sontag_cdc2018.pdf},
ABSTRACT = {The primary factor limiting the success of chemotherapy
in cancer treatment is the phenomenon of drug resistance. This work
extends the work reported in "A mathematical approach to distinguish
spontaneous from induced evolution of drug resistance during cancer
treatment" by introducing a time-optimal control problem that is
analyzed utilizing differential-geometric techniques: we seek a
treatment protocol which maximizes the time of treatment until a
critical tumor size is reached. The general optimal control structure
is determined as a combination of both bang-bang and path-constrained
arcs. Numerical results are presented which demonstrate decreasing
treatment efficacy as a function of the ability of the drug to induce
resistance. Thus, drug-induced resistance may dramatically effect the
outcome of chemotherapy, implying that factors besides cytotoxicity
should be considered when designing treatment regimens.}
}
@INPROCEEDINGS{18cdc_tutorial_imp,
AUTHOR = {J. Huang and A. Isidori and L. Marconi and M. Mischiati and
E. D. Sontag and W. M. Wonham},
BOOKTITLE = {Proc. 2018 IEEE Conf. Decision and Control},
TITLE = {Internal models in control, biology and neuroscience},
YEAR = {2018},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5370-5390},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {feeedback, internal model principle, nonlinear systems,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/huang_isidori_marconi_mischiati_sontag_wonham_internal_model_cdc2018.pdf},
ABSTRACT = {This tutorial paper deals with the Internal Model
Principle (IMP) from different perspectives. The goal is to start
from the principle as introduced and commonly used in the control
theory and then enlarge the vision to other fields where "internal
models" play a role. The biology and neuroscience fields are
specifically targeted in the paper. The paper ends by presenting an
"abstract" theory of IMP applicable to a large class of systems.}
}
@INPROCEEDINGS{18cdc_margaliot,
AUTHOR = {M. Margaliot and E.D. Sontag},
BOOKTITLE = {Proc. 2018 IEEE Conf. Decision and Control},
TITLE = {Analysis of nonlinear tridiagonal cooperative systems
using totally positive linear differential systems},
YEAR = {2018},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3104-3109},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {tridiagonal systems, cooperative systems,
monotone systems},
PDF = {../../FTPDIR/margaliot_sontag_cdc2018.pdf},
ABSTRACT = {This is a conference version of "Revisiting totally
positive differential systems: A tutorial and new results".}
}
@TECHREPORT{greene_sanchez_sontag_biorxiv_nov2018,
AUTHOR = {J.M. Greene and C. Sanchez-Tapia and E.D. Sontag},
INSTITUTION = {bioRxiv 2018/475533},
TITLE = {Mathematical details on a cancer resistance model},
YEAR = {2018},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {identifiability, drug resistance, chemotherapy,
optimal control theory, singular controls, oncology, cancer},
PDF = {../../FTPDIR/2018_11_greene_sanchez_sontag_cancer_resistance_biorxiv.pdf},
ABSTRACT = {The primary factor limiting the success of chemotherapy
in cancer treatment is the phenomenon of drug resistance. We have
recently introduced a framework for quantifying the effects of
induced and non-induced resistance to cancer chemotherapy . In this
work, the control structure is precisely characterized as a
concatenation of bang-bang and path-constrained arcs via the
Pontryagin Maximum Principle and differential Lie techniques. A
structural identfiability analysis is also presented, demonstrating
that patient-specfic parameters may be measured and thus utilized in
the design of optimal therapies prior to the commencement of therapy.}
}
@TECHREPORT{arxiv_periodic_rfm_dec2018,
AUTHOR = {M. Sadeghi and M.A. Al-Radhawi and M. Margaliot and
E.D. Sontag},
INSTITUTION = {bioRxiv 2018/507988},
TITLE = {On the periodic gain of the Ribosome Flow Model},
YEAR = {2018},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {systems biology, reaction networks, ribosomes, RFM,
ribosome flow model},
PDF = {../../FTPDIR/2018_12_sadeghi_alradhawi_margaliot_sontag_rfm_periodic_biorxiv.pdf},
ABSTRACT = {We consider a compartmental model for ribosome flow
during RNA translation, the Ribosome Flow Model (RFM). This model
includes a set of positive transition rates that control the flow
from every site to the consecutive site. It has been shown that when
these rates are time-varying and jointly T-periodic, the protein
production rate converges to a unique T-periodic pattern. Here, we
study a problem that can be roughly stated as: can periodic rates
yield a higher average production rate than constant rates? We
rigorously formulate this question and show via simulations, and
rigorous analysis in one simple case, that the answer is no.}
}
@INCOLLECTION{margaliot_tuller_sontag_pralyfestbook_2016,
AUTHOR = {M. Margaliot and E.D. Sontag and T. Tuller},
BOOKTITLE = {Feedback Stabilization of Controlled Dynamical Systems - In Honor of Laurent Praly},
PUBLISHER = {Springer-Verlag},
TITLE = {Checkable conditions for contraction after small
transients in time and amplitude},
YEAR = {2017},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {N. Petit},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {279-305},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {473},
KEYWORDS = {contractions, contractive systems, stability},
PDF = {../../FTPDIR/margaliot_tuller_sontag_contractions_pralybook_2017.pdf},
ABSTRACT = {This is an expository paper, which compares in detail
various alternative weak contraction ideas for nonlinear system
stability.}
}
@ARTICLE{gevertz2017bootstrap,
AUTHOR = {S. Barish and M.F. Ochs and E.D. Sontag and J.L. Gevertz},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Evaluating optimal therapy robustness by virtual
expansion of a sample population, with a case study in cancer
immunotherapy},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {E6277-E6286},
VOLUME = {114},
KEYWORDS = {cancer, oncolytic therapy, immunotherapy,
optimal therapy, identifiability, systems biology},
URL = {http://www.pnas.org/content/early/2017/07/14/1703355114.abstract},
PDF = {../../FTPDIR/barish_ochs_sontag_gevertz_optimal_therapy_robustness_pnas2017.pdf},
ABSTRACT = {This paper proposes a technique that combines
experimental data, mathematical modeling, and statistical analyses
for identifying optimal treatment protocols that are robust with
respect to individual variability. Experimental data from a small
sample population is amplified using bootstrapping to obtain a large
number of virtual populations that statistically match the expected
heterogeneity. Alternative therapies chosen from among a set of
clinically-realizable protocols are then compared and scored
according to coverage. As proof of concept, the method is used to
evaluate a treatment with oncolytic viruses and dendritic cell
vaccines in a mouse model of melanoma. The analysis shows that while
every scheduling variant of an experimentally-utilized treatment
protocol is fragile (non-robust), there is an alternative region of
dosing space (lower oncolytic virus dose, higher dendritic cell dose)
for which a robust optimal protocol exists.},
DOI = {10.1073/pnas.1703355114}
}
@ARTICLE{kim2017,
AUTHOR = {J. K. Kim and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Reduction of multiscale stochastic biochemical reaction
networks using exact moment derivation},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {13(6): e1005571},
VOLUME = {13},
KEYWORDS = {systems biology, reaction networks, stochastic systems,
chemical master equation, reaction networks, reaction networks,
moments, molecular networks, complex-balanced networks},
PDF = {../../FTPDIR/kim_sontag_2017_plos_cb_with_supplement.pdf},
ABSTRACT = {Biochemical reaction networks in cells frequently
consist of reactions with disparate timescales. Stochastic
simulations of such multiscale BRNs are prohibitively slow due to the
high computational cost incurred in the simulations of fast
reactions. One way to resolve this problem is to replace fast species
by their stationary conditional expectation values conditioned on
slow species. While various approximations schemes for this
quasi-steady state approximation have been developed, they often lead
to considerable errors. This paper considers two classes of
multiscale BRNs which can be reduced by through an exact QSS rather
than approximations. Specifically, we assume that fast species
constitute either a feedforward network or a complex balanced
network. Exact reductions for various examples are derived, and the
computational advantages of this approach are illustrated through
simulations.}
}
@ARTICLE{lang_sontag_automatica_2016,
AUTHOR = {M. Lang and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Zeros of nonlinear systems with input invariances},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {46-55},
VOLUME = {81},
KEYWORDS = {scale invariance, fold change detection,
nonlinear systems, realization theory, internal model principle},
PDF = {../../FTPDIR/lang_sontag_zeros_nonlinear_systems_automatica_2017.pdf},
ABSTRACT = {This paper introduces two generalizations of systems
invariant with respect to continuous sets of input transformations,
that is, systems whose output dynamics remain invariant when applying
a transformation to the input and simultaneously adjusting the
initial conditions. These generalizations concern systems invariant
with respect to time-dependent input transformations with
exponentially increasing or decreasing ``strength'', and systems
invariant with respect to transformations of the "nonlinear
derivatives" of the input. Interestingly, these two generalizations
of invariant systems encompass linear time-invariant (LTI) systems
with real transfer function zeros of arbitrary multiplicity.
Furthermore, the zero-dynamics of systems possessing our generalized
invariances show properties analogous to those of LTI systems with
transfer function zeros, generalizing concepts like pole-zero
cancellation, the rejection of ramps by Hurwitz LTI systems with a
zero at the origin with multiplicity two, and (to a certain extend)
the superposition principle with respect to inputs zeroing the
output.}
}
@ARTICLE{16menolascina_et_al_journal,
AUTHOR = {F. Menolascina and R. Rusconi and V.I. Fernandez and
S.P. Smriga and Z. Aminzare and E. D. Sontag and R. Stocker},
JOURNAL = {npj Systems Biology and Applications},
TITLE = {Logarithmic sensing in Bacillus subtilis aerotaxis},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {16036-},
VOLUME = {3},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
Aerotaxis, chemotaxis, scale invariance, FCD, fold-change detection,
B. subtilis, systems biology},
PDF = {../../FTPDIR/menolascina_at_al_logarithmic_sensing_b_subtilis_aerotaxis_npjsysbio_2017_with_SI.pdf},
ABSTRACT = {Aerotaxis, the directed migration along oxygen
gradients, allows many microorganisms to locate favorable oxygen
concentrations. Despite oxygen's fundamental role for life, even key
aspects of aerotaxis remain poorly understood. In Bacillus subtilis,
for example, there is conflicting evidence of whether migration
occurs to the maximal oxygen concentration available or to an optimal
intermediate one, and how aerotaxis can be maintained over a broad
range of conditions. Using precisely controlled oxygen gradients in a
microfluidic device, spanning the full spectrum of conditions from
quasi-anoxic to oxic (60nM-1mM), we resolved B. subtilis' ``oxygen
preference conundrum'' by demonstrating consistent migration towards
maximum oxygen concentrations. Surprisingly, the strength of
aerotaxis was largely unchanged over three decades in oxygen
concentration (131nM-196mM). We discovered that in this range B.
subtilis responds to the logarithm of the oxygen concentration
gradient, a log-sensing strategy that affords organisms high
sensitivity over a wide range of conditions.}
}
@ARTICLE{txtl2017,
AUTHOR = {V. H. Nagaraj and J. M. Greene and A. M. Sengupta and
E.D. Sontag},
JOURNAL = {Synthetic Biology},
TITLE = {Translation inhibition and resource balance in the TX-TL
cell-free gene expression system},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {ysx005},
VOLUME = {2},
KEYWORDS = {tx/tl, cell-free systems, in vitro synthetic biology,
synthetic biology, systems biology},
PDF = {../../FTPDIR/nagaraj_greene_sengupta_sontag_reprint_2017.pdf},
ABSTRACT = {Utilizing the synthetic transcription-translation
(TX-TL) system, this paper studies the impact of nucleotide
triphosphates (NTPs) and magnesium (Mg2+), on gene expression, in the
context of the counterintuitive phenomenon of suppression of gene
expression at high NTP concentration. Measuring translation rates for
different Mg2+ and NTP concentrations, we observe a complex resource
dependence. We demonstrate that translation is the rate-limiting
process that is directly inhibited by high NTP concentrations.
Additional Mg2+ can partially reverse this inhibition. In several
experiments, we observe two maxima of the translation rate viewed as
a function of both Mg2+ and NTP concentration, which can be explained
in terms of an NTP-independent effect on the ribosome complex and an
NTP- Mg2+ titration effect. The non-trivial compensatory effects of
abundance of different vital resources signals the presence of
complex regulatory mechanisms to achieve optimal gene expression.}
}
@ARTICLE{rahi2017,
AUTHOR = {S. J. Rahi and J. Larsch and K. Pecani and N. Mansouri and
A. Y. Katsov and K. Tsaneva-Atanasova and E. D. Sontag and
F. R. Cross},
JOURNAL = {Nature Methods},
TITLE = {Oscillatory stimuli differentiate adapting circuit
topologies},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1010-1016},
VOLUME = {14},
KEYWORDS = {entrainment, systems biology, periodic inputs,
subharmonic responses, biochemical systems, forced oscillations,
reaction networks, periodic behaviors, monotone systems,
oscillations, incoherent feedforward loop, feedforward, IFFL,
systems biology},
PDF = {../../FTPDIR/rahi_et_al_nature_methods_2017_reprint.pdf},
ABSTRACT = {Elucidating the structure of biological intracellular
networks from experimental data remains a major challenge. This paper
studies two types of ``response signatures'' to identify specific
circuit motifs, from the observed response to periodic inputs. In
particular, the objective is to distinguish negative feedback loops
(NFLs) from incoherent feedforward loops (IFFLs), which are two types
of circuits capable of producing exact adaptation. The theory of
monotone systems with inputs is used to show that ``period skipping''
(non-harmonic responses) is ruled out in IFFL's, and a notion called
``refractory period stabilization'' is also analyzed. The approach is
then applied to identify a circuit dominating cell cycle timing in
yeast, and to uncover a calcium-mediated NFL circuit in
\emph{C.elegans} olfactory sensory neurons.}
}
@ARTICLE{2017rendall_sontag,
AUTHOR = {A. Rendall and E. D. Sontag},
JOURNAL = {Royal Society Open Science},
TITLE = {Multiple steady states and the form of response
functions to antigen in a model for the initiation of T cell
activation},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {170821-},
VOLUME = {4},
KEYWORDS = {kinetic proofreading, T cells, immunology,
systems biology},
PDF = {../../FTPDIR/2017_rendall_sontag_tcells_royal_open_reprint.pdf},
ABSTRACT = {This paper analizes a model for the initial stage of T
cell activation. The state variables in the model are the
concentrations of phosphorylation states of the T cell receptor
complex and the phosphatase SHP-1 in the cell. It is shown that these
quantities cannot approach zero, and that there is more than one
positive steady state for certain values of the parameters; in
addition, damped oscillations are possible. It is also shown that the
chemical concentration which represents the degree of activation of
the cell, represented by the maximally phosphorylated form of the T
cell receptor complex, is in general a non-monotone function of the
activating signal. In particular there are cases where there is a
value of the dissociation constant of the ligand from the receptor
which produces an optimal activation of the T cell. In this way the
results of certain simulations in the literature have been confirmed
rigorously and new features are discovered.}
}
@ARTICLE{silva2017,
AUTHOR = {A. Silva and M. Silva and P. Sudalagunta and A. Distler and
T. Jacobson and A. Collins and T. Nguyen and J. Song and D.T. Chen and
Lu Chen and C. Cubitt and R. Baz and L. Perez and D. Rebatchouk and
W. Dalton and J.M. Greene and R. Gatenby and R. Gillies and
E.D. Sontag and M. Meads and K. Shain},
JOURNAL = {Cancer Research},
TITLE = {An ex vivo platform for the prediction of clinical
response in multiple myeloma},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {10.1158/0008-5472.CAN-17-0502},
OPTVOLUME = {},
KEYWORDS = {cancer, multiple myeloma, personalized therapy},
PDF = {../../FTPDIR/2019_silva_et_al_cancer_research_myeloma.pdf},
ABSTRACT = {This paper describes a novel approach for
characterization of chemosensitivity and prediction of clinical
response in multiple myeloma. It relies upon a patient-specific
computational model of clinical response, parameterized by a
high-throughput ex vivo assay that quantifies sensitivity of primary
MM cells to 31 agents or combinations, in a reconstruction of the
tumor microenvironment. The mathematical model, which inherently
accounts for intra-tumoral heterogeneity of drug sensitivity,
combined with drug- and regimen-specific pharmacokinetics, produces
patient-specific predictions of clinical response 5 days post-biopsy.}
}
@ARTICLE{two-zone-journal,
AUTHOR = {E.D. Sontag},
JOURNAL = {Cell Systems},
TITLE = {A dynamical model of immune responses to antigen
presentation predicts different regions of tumor or pathogen
elimination},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {231-241},
VOLUME = {4},
KEYWORDS = {scale invariance, fold change detection, T cells,
incoherent feedforward loops, immunology, cancer,
internal model principle, incoherent feedforward loop, feedforward,
IFFL, systems biology},
PDF = {../../FTPDIR/sontag_cell_systems2017_dynamical_model_immune.pdf},
ABSTRACT = {Since the early 1990s, many authors have independently
suggested that self/nonself recognition by the immune system might be
modulated by the rates of change of antigen challenges. This paper
introduces an extremely simple and purely conceptual mathematical
model that allows dynamic discrimination of immune challenges. The
main component of the model is a motif which is ubiquitous in systems
biology, the incoherent feedforward loop, which endows the system
with the capability to estimate exponential growth exponents, a
prediction which is consistent with experimental work showing that
exponentially increasing antigen stimulation is a determinant of
immune reactivity. Combined with a bistable system and a simple
feedback repression mechanism, an interesting phenomenon emerges as a
tumor growth rate increases: elimination, tolerance (tumor growth),
again elimination, and finally a second zone of tolerance (tumor
escape). This prediction from our model is analogous to the
``two-zone tumor tolerance'' phenomenon experimentally validated
since the mid 1970s. Moreover, we provide a plausible biological
instantiation of our circuit using combinations of regulatory and
effector T cells. }
}
@ARTICLE{plos2017_dynamic_compensation,
AUTHOR = {E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Dynamic compensation, parameter identifiability, and
equivariances},
YEAR = {2017},
OPTMONTH = {},
NOTE = {(Preprint was in bioRxiv https://doi.org/0.1101/095828, 2016)},
OPTNUMBER = {},
PAGES = {e1005447},
VOLUME = {13},
KEYWORDS = {fcd, fold-change detection, scale invariance,
dynamic compensation, identifiability, observability,
systems biology},
URL = {https://doi.org/10.1371/journal.pcbi.1005447},
PDF = {../../FTPDIR/dynamic_compensation_parameter_identifiability_equivariances_sontag_plos2017.pdf},
ABSTRACT = {A recent paper by Karin et al. introduced a mathematical
notion called dynamical compensation (DC) of biological circuits. DC
was shown to play an important role in glucose homeostasis as well as
other key physiological regulatory mechanisms. Karin et al.\ went on
to provide a sufficient condition to test whether a given system has
the DC property. Here, we show how DC is a reformulation of a
well-known concept in systems biology, statistics, and control theory
-- that of parameter structural non-identifiability. Viewing DC as a
parameter identification problem enables one to take advantage of
powerful theoretical and computational tools to test a system for DC.
We obtain as a special case the sufficient criterion discussed by
Karin et al. We also draw connections to system equivalence and to
the fold-change detection property.}
}
@ARTICLE{solving_immunology2016,
AUTHOR = {Y. Vodovotz and A. Xia and E. Read and
J. Bassaganya-Riera and D.A. Hafler and E.D. Sontag and J. Wang and
J.S. Tsang and J.D. Day and S. Kleinstein and A.J. Butte and
M.C. Altman and R. Hammond and C. Benoist and S.C. Sealfon},
JOURNAL = {Trends in Immunology},
TITLE = {Solving Immunology?},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {116-127},
VOLUME = {38},
KEYWORDS = {Immunology},
PDF = {../../FTPDIR/2016_solving_immunology_in_press.pdf},
ABSTRACT = {Emergent responses of the immune system result from the
integration of molecular and cellular networks over time and across
multiple organs. High-content and high-throughput analysis
technologies, concomitantly with data-driven and mechanistic
modeling, hold promise for the systematic interrogation of these
complex pathways. However, connecting genetic variation and molecular
mechanisms to individual phenotypes and health outcomes has proven
elusive. Gaps remain in data, and disagreements persist about the
value of mechanistic modeling for immunology. This paper presents
perspectives that emerged from the National Institute of Allergy and
Infectious Disease (NIAID) workshop `Complex Systems Science,
Modeling and Immunity' and subsequent discussions regarding the
potential synergy of high-throughput data acquisition, data-driven
modeling, and mechanistic modeling to define new mechanisms of
immunological disease and to accelerate the translation of these
insights into therapies.}
}
@ARTICLE{yang_khare-enzyme_assemblies2017,
AUTHOR = {L. Yang and E.M. Dolan and S.K. Tan and T. Lin and
E.D. Sontag and S.D. Khare},
JOURNAL = {ChemBioChem},
TITLE = {Computation-guided design of a stimulus-responsive
multi-enzyme supramolecular assembly, systems biology},
YEAR = {2017},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2000-2006},
VOLUME = {18},
PDF = {../../FTPDIR/yang_et_al_sontag_khare_multienzyme_chembiochem2017.pdf},
ABSTRACT = {This paper reports on the construction of a
phosphorylation- and optically-responsive supramolecular complex of
metabolic pathway enzymes for the biodegradation of an environmental
pollutant. Fusing of enzymes led to an increase in pathway
efficiency, and illustrates the possibility of spatio-temporal
control over formation and functioning of a wide variety of synthetic
biotransformations.}
}
@ARTICLE{aminzare_sontag_pde2015,
AUTHOR = {Z. Aminzare and E.D. Sontag},
JOURNAL = {Nonlinear Analysis},
TITLE = {Some remarks on spatial uniformity of solutions of
reaction-diffusion PDEs},
YEAR = {2016},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {125-144},
VOLUME = {147},
KEYWORDS = {contractions, contractive systems, matrix measures,
logarithmic norms, synchronization, consensus,
reaction-diffusion PDEs, partial differential equations},
PDF = {../../FTPDIR/aminzare_sontag_nonlinear_analysis_2016_reprint.pdf},
ABSTRACT = {This paper presents a condition which guarantees spatial
uniformity for the asymptotic behavior of the solutions of a reaction
diffusion partial differential equation (PDE) with Neumann boundary
conditions in one dimension, using the Jacobian matrix of the
reaction term and the first Dirichlet eigenvalue of the Laplacian
operator on the given spatial domain. The estimates are based on
logarithmic norms in non-Hilbert spaces, which allow, in particular
for a class of examples of interest in biology, tighter estimates
than other previously proposed methods.}
}
@ARTICLE{igoshin_et_al2015_monotone,
AUTHOR = {J.A. Ascensao and P. Datta and B. Hancioglu and
E.D. Sontag and M.L. Gennaro and O.A. Igoshin},
JOURNAL = {PLoS Computational Biology},
TITLE = {Non-monotonic response dynamics of glyoxylate shunt
genes in Mycobacterium tuberculosis},
YEAR = {2016},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1004741},
VOLUME = {12},
KEYWORDS = {cell signaling, monotone systems, monotone systems,
systems biology},
PDF = {../../FTPDIR/monotone_tb_sontag_igoshin_plos2016.pdf},
ABSTRACT = {Understanding how dynamical responses of biological
networks are constrained by underlying network topology is one of the
fundamental goals of systems biology. Here we employ monotone systems
theory to formulate a theorem stating necessary conditions for
non-monotonic time-response of a biochemical network to a monotonic
stimulus. We apply this theorem to analyze the non-monotonic dynamics
of the sigmaB-regulated glyoxylate shunt gene expression in
Mycobacterium tuberculosis cells exposed to hypoxia. We first
demonstrate that the known network structure is inconsistent with
observed dynamics. To resolve this inconsistency we employ the
formulated theorem, modeling simulations and optimization along with
follow-up dynamic experimental measurements. We show a requirement
for post-translational modulation of sigmaB activity in order to
reconcile the network dynamics with its topology. The results of this
analysis make testable experimental predictions and demonstrate wider
applicability of the developed methodology to a wide class of
biological systems.}
}
@ARTICLE{margaliot_sontag_tuller_cast_2015,
AUTHOR = {M. Margaliot and E.D. Sontag and T. Tuller},
JOURNAL = {Automatica},
TITLE = {Contraction after small transients},
YEAR = {2016},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {178-184},
VOLUME = {67},
KEYWORDS = {entrainment, nonlinear systems, stability, contractions,
contractive systems, systems biology},
PDF = {../../FTPDIR/margaliot_sontag_tuller_automatica2016.pdf},
ABSTRACT = {Contraction theory is a powerful tool for proving
asymptotic properties of nonlinear dynamical systems including
convergence to an attractor and entrainment to a periodic excitation.
We introduce three new forms of generalized contraction (GC) that are
motivated by allowing contraction to take place after small
transients in time and/or amplitude. These forms of GC are useful for
several reasons. First, allowing small transients does not destroy
the asymptotic properties provided by standard contraction. Second,
in some cases as we change the parameters in a contractive system it
becomes a GC just before it looses contractivity. In this respect, GC
is the analogue of marginal stability in Lyapunov stability theory.
We provide checkable sufficient conditions for GC, and demonstrate
their usefulness using several models from systems biology that are
not contractive, with respect to any norm, yet are GC.}
}
@ARTICLE{nikolaev_sontag_quorum_toggle_2015,
AUTHOR = {E.V. Nikolaev and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Quorum-sensing synchronization of synthetic toggle
switches: A design based on monotone dynamical systems theory},
YEAR = {2016},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1004881},
VOLUME = {12},
KEYWORDS = {quorum sensing, toggle switches, monotone systems,
systems biology},
PDF = {../../FTPDIR/nikolaev_sontag_toggle_quorum_ploscb_2016.pdf},
ABSTRACT = {Synthetic constructs in biotechnology, bio-computing,
and proposed gene therapy interventions are often based on plasmids
or transfected circuits which implement some form of on-off (toggle
or flip-flop) switch. For example, the expression of a protein used
for therapeutic purposes might be triggered by the recognition of a
specific combination of inducers (e.g., antigens), and memory of this
event should be maintained across a cell population until a specific
stimulus commands a coordinated shut-off. The robustness of such a
design is hampered by molecular (intrinsic) or environmental
(extrinsic) noise, which may lead to spontaneous changes of state in
a subset of the population and is reflected in the bimodality of
protein expression, as measured for example using flow cytometry. In
this context, a majority-vote correction circuit, which brings
deviant cells back into the required state, is highly desirable. To
address this concrete challenge, we have developed a new theoretical
design for quorum-sensing (QS) synthetic toggles. QS provides a way
for cells to broadcast their states to the population as a whole so
as to facilitate consensus. Our design is endowed with strong
theoretical guarantees, based on monotone dynamical systems theory,
of global stability and no oscillations, and which leads to robust
consensus states.}
}
@ARTICLE{raveh_margaliot_sontag_tuller_ribosome_compete_arxiv_2015,
AUTHOR = {A. Raveh and M. Margaliot and E.D. Sontag and T. Tuller},
JOURNAL = {Proc. Royal Society Interface},
TITLE = {A model for competition for ribosomes in the cell},
YEAR = {2016},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2015.1062},
VOLUME = {13},
KEYWORDS = {resource competition, ribosomes, entrainment,
nonlinear systems, stability, contractions, contractive systems,
systems biology, RFM, ribosome flow model},
PDF = {../../FTPDIR/raveh_margaliot_sontag_tuller_ribosome_competition_interface2016.pdf},
ABSTRACT = {We develop and analyze a general model for large-scale
simultaneous mRNA translation and competition for ribosomes. Such
models are especially important when dealing with highly expressed
genes, as these consume more resources. For our model, we prove that
the compound system always converges to a steady-state and that it
always entrains or phase locks to periodically time-varying
transition rates in any of the mRNA molecules. We use this model to
explore the interactions between the various mRNA molecules and
ribosomes at steady-state. We show that increasing the length of an
mRNA molecule decreases the production rate of all the mRNAs.
Increasing any of the codon translation rates in a specific mRNA
molecule yields a local effect: an increase in the translation rate
of this mRNA, and also a global effect: the translation rates in the
other mRNA molecules all increase or all decrease. These results
suggest that the effect of codon decoding rates of endogenous and
heterologous mRNAs on protein production might be more complicated
than previously thought.}
}
@INPROCEEDINGS{16acc_lang_sontag,
AUTHOR = {M. Lang and E.D. Sontag},
BOOKTITLE = {2016 American Control Conference (ACC)},
TITLE = {Scale-invariant systems realize nonlinear differential
operators},
YEAR = {2016},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {6676 - 6682},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {scale invariance, fold change detection,
nonlinear systems, realization theory, internal model principle},
PDF = {../../FTPDIR/16acc_lang_sontag_published.pdf},
ABSTRACT = {In this article, we show that scale-invariant systems,
as well as systems invariant with respect to other input
transformations, can realize nonlinear differential operators: when
excited by inputs obeying functional forms characteristic for a given
class of invariant systems, the systems' outputs converge to constant
values directly quantifying the speed of the input.}
}
@INPROCEEDINGS{16cdc_menolascina,
AUTHOR = {F. Menolascina and R. Stocker and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Dec. 2016},
TITLE = {In-vivo identification and control of aerotaxis in
Bacillus subtilis},
YEAR = {2016},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {764-769},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identification, systems biology, aerotaxis, B. subtilis},
PDF = {../../FTPDIR/2016cdc_menolascina_stocker_sontag_as_published.pdf},
ABSTRACT = {Combining in-vivo experiments with system identification
methods, we determine a simple model of aerotaxis in B. subtilis, and
we subsequently employ this model in order to compute the sequence of
oxygen gradients needed in order to achieve set-point regulation with
respect to a signal tracking the center of mass of the bacterial
population. We then successfully validate both the model and the
control scheme, by showing that in-vivo positioning control can be
achieved via the application of the precomputed inputs in-vivo in an
open-loop configuration.}
}
@INPROCEEDINGS{16cdc_immune,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Dec. 2016},
TITLE = {Some remarks on a model for immune signal detection and
feedback},
YEAR = {2016},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2475-2480},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {scale invariance, fold change detection, T cells,
incoherent feedforward loops, immunology, cancer},
PDF = {../../FTPDIR/2016cdc_immune_as_published.pdf},
ABSTRACT = {This is a conference paper related to the journal paper
"A dynamical model of immune responses to antigen presentation
predicts different regions of tumor or pathogen elimination". The
conference paper includes several theorems for a simplified model
which were not included in the journal paper.}
}
@INPROCEEDINGS{16cdc_bleris,
AUTHOR = {Q. Tyles and T. Kang and E.D. Sontag and L. Bleris},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Dec. 2016},
TITLE = {Exploring the impact of resource limitations on gene
network reconstruction},
YEAR = {2016},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3350-3355},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {Biological systems, Genetic regulatory systems,
Systems biology},
PDF = {../../FTPDIR/2016cdc_quarton_kang_sontag_bleris},
ABSTRACT = {Applying Modular Response Analysis to a synthetic gene
circuit, which was introduced in a recent paper by the authors, leads
to the inference of a nontrivial "ghost" regulation edge which was
not explicitly engineered into the network and which is, in fact, not
immediately apparent from experimental measurements. One may thus
hypothesize that this ghost regulatory effect is due to competition
for resources. A mathematical model is proposed, and analyzed in
closed form, that lends validation to this hypothesis.}
}
@INPROCEEDINGS{16cdc_rfm_control,
AUTHOR = {Y. Zarai and M. Margaliot and E.D. Sontag and T. Tuller},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Dec. 2016},
TITLE = {Controlling the ribosomal density profile in mRNA
translation},
YEAR = {2016},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4184-4189},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {ribosomes, translation, RFM, ribosome flow model}
}
@TECHREPORT{arxiv_iffl_jan2016,
AUTHOR = {E.D. Sontag},
INSTITUTION = {arXiv:1602.00162},
TITLE = {A remark on incoherent feedforward circuits as change
detectors and feedback controllers},
YEAR = {2016},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {scale invariance, fold change detection, T cells,
incoherent feedforward loops, immunology,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/arxiv_iffl_change_detection_jan2016_1602.00162v1.pdf},
ABSTRACT = {This note analyzes incoherent feedforward loops in
signal processing and control. It studies the response properties of
IFFL's to exponentially growing inputs, both for a standard version
of the IFFL and for a variation in which the output variable has a
positive self-feedback term. It also considers a negative feedback
configuration, using such a device as a controller. It uncovers a
somewhat surprising phenomenon in which stabilization is only
possible in disconnected regions of parameter space, as the
controlled system's growth rate is varied.}
}
@TECHREPORT{arxiv_moments_dec2016,
AUTHOR = {E.D. Sontag},
INSTITUTION = {arXiv:1612.02393},
TITLE = {Examples of computation of exact moment dynamics for
chemical reaction networks},
YEAR = {2016},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {systems biology, reaction networks, stochastic systems,
chemical master equation, reaction networks, reaction networks,
moments, molecular networks, complex-balanced networks},
PDF = {http://arxiv.org/abs/1612.02393},
ABSTRACT = {We review in a unified way results for two types of
stochastic chemical reaction systems for which moments can be
effectively computed: feedforward networks and complex-balanced
networks.}
}
@TECHREPORT{biorxiv_two_zone_dec2016,
AUTHOR = {E.D. Sontag},
INSTITUTION = {bioRxiv https://doi.org/10.1101/095455},
TITLE = {Two-zone tumor tolerance can arise from a simple
immunological feedforward motif that estimates tumor growth rates},
YEAR = {2016},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {scale invariance, fold change detection, T cells,
incoherent feedforward loops, immunology, cancer},
PDF = {http://biorxiv.org/content/biorxiv/early/2016/12/20/095455.full.pdf},
ABSTRACT = {Preprint version of "A dynamical model of immune
responses to antigen presentation predicts different regions of tumor
or pathogen elimination", appeared in Cell Systems 2017. However, the
journal version does not include Section 9 on degradation-based
IFFL's from this preprint.}
}
@INCOLLECTION{iss_encyclopedia_systems_control2015,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Encyclopedia of Systems and Control},
PUBLISHER = {Springer-Verlag},
TITLE = {Input-to-State Stability},
YEAR = {2015},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {J. Baillieul and T. Samad},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
input to output stability},
PDF = {../../FTPDIR/2015_sontag_iss_encyclopedia_systems_control_whiteout.pdf},
ABSTRACT = {The notion of input to state stability (ISS)
qualitatively describes stability of the mapping from initial states
and inputs to internal states (and more generally outputs). This
entry focuses on the definition of ISS and a discussion of equivalent
characterizations.}
}
@ARTICLE{kholodenko_naturebiotech_2015_letter,
AUTHOR = {P. Bastiaens and M. R. Birtwistle and N. Bluthgen and
F. J. Bruggeman and K.-H. Cho and C. Cosentino and de la Fuente, A. and
J. B. Hoek and A. Kiyatkin and S. Klamt and W. Kolch and S. Legewie and
P. Mendes and T. Naka and T. Santra and E.D. Sontag and
H. V. Westerhoff and B. N. Kholodenko},
JOURNAL = {Nature Biotech},
TITLE = {Silence on the relevant literature and errors in
implementation},
YEAR = {2015},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {336-339},
VOLUME = {33},
KEYWORDS = {modular response analysis, systems biology,
reaction networks, reverse engineering, gene and protein networks,
protein networks, gene networks, systems identification},
PDF = {../../FTPDIR/bastiaens_et_al_kholodenko_about_barabasi_nature_biotech2015.pdf},
ABSTRACT = {This letter discusses a paper in the same journal which
reported a method for reconstructing network topologies. Here we show
that the method is a variant of a previously published method,
modular response analysis. We also demonstrate that the
implementation of the algorithm in that paper using statistical
similarity measures as a proxy for global network responses to
perturbations is erroneous and its performance is overestimated.}
}
@ARTICLE{15bleris_direct_indirect,
AUTHOR = {T. Kang and R. Moore and Y. Li and E.D. Sontag and
L. Bleris},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Discriminating direct and indirect connectivities in
biological networks},
YEAR = {2015},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {12893-12898},
VOLUME = {112},
KEYWORDS = {modular response analysis, stochastic systems,
reverse engineering, gene networks, synthetic biology, feedforward,
systems biology},
PDF = {../../FTPDIR/kang_moore_li_sontag_bleris2015.pdf},
ABSTRACT = {Reverse engineering of biological pathways involves an
iterative process between experiments, data processing, and
theoretical analysis. In this work, we engineer synthetic circuits,
subject them to perturbations, and then infer network connections
using a combination of nonparametric single-cell data resampling and
modular response analysis. Intriguingly, we discover that recovered
weights of specific network edges undergo divergent shifts under
differential perturbations, and that the particular behavior is
markedly different between different topologies. Investigating
topological changes under differential perturbations may address the
longstanding problem of discriminating direct and indirect
connectivities in biological networks.}
}
@ARTICLE{skataric_nikolaev_fcd1,
AUTHOR = {M. Skataric and E.V. Nikolaev and E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {A fundamental limitation to fold-change detection by
biological systems with multiple time scales},
YEAR = {2015},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1-15},
VOLUME = {9},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
singular perturbations, scale invariance, systems biology,
transient behavior, symmetries, fcd, fold-change detection,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/2015_skataric_nikoloaev_sontag_fcd_iet2015.pdf},
ABSTRACT = {The phenomenon of fold-change detection, or scale
invariance, is exhibited by a variety of sensory systems, in both
bacterial and eukaryotic signaling pathways. It has been often
remarked in the systems biology literature that certain systems whose
output variables respond at a faster time scale than internal
components give rise to an approximate scale-invariant behavior,
allowing approximate fold-change detection in stimuli. This paper
establishes a fundamental limitation of such a mechanism, showing
that there is a minimal fold-change detection error that cannot be
overcome, no matter how large the separation of time scales is. To
illustrate this theoretically predicted limitation, we discuss two
common biomolecular network motifs, an incoherent feedforward loop
and a feedback system, as well as a published model of the chemotaxis
signaling pathway of Dictyostelium discoideum.}
}
@ARTICLE{sontag_singh_june2015,
AUTHOR = {E.D. Sontag and A. Singh},
JOURNAL = {IEEE Life Sciences Letters},
TITLE = {Exact moment dynamics for feedforward nonlinear chemical
reaction networks},
YEAR = {2015},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {26-29},
VOLUME = {1},
KEYWORDS = {systems biology, reaction networks, stochastic systems,
chemical master equation, reaction networks, reaction networks},
PDF = {../../FTPDIR/sontag_singh_moments_ieee_life_sciences2015.pdf},
ABSTRACT = {Chemical systems are inherently stochastic, as reactions
depend on random (thermal) motion. This motivates the study of
stochastic models, and specifically the Chemical Master Equation
(CME), a discrete-space continuous-time Markov process that describes
stochastic chemical kinetics. Exact studies using the CME are
difficult, and several moment closure tools related to "mass
fluctuation kinetics" and "fluctuation-dissipation" formulas can be
used to obtain approximations of moments. This paper, in contrast,
introduces a class of nonlinear chemical reaction networks for which
exact computation is possible, by means of finite-dimensional linear
differential equations. This class allows second and higher order
reactions, but only under special assumptions on structure and/or
conservation laws.}
}
@ARTICLE{14sgt_freitas_sontag,
AUTHOR = {de Freitas, M. Marcondes and E.D. Sontag},
JOURNAL = {SIAM J. Control and Optimization},
TITLE = {A small-gain theorem for random dynamical systems with
inputs and outputs},
YEAR = {2015},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2657-2695},
VOLUME = {53},
KEYWORDS = {random dynamical systems, monotone systems,
small-gain theorem, stochastic systems},
PDF = {../../FTPDIR/freitas_sontag_siam2015_reprint.pdf},
ABSTRACT = {A formalism for the study of random dynamical systems
with inputs and outputs (RDSIO) is introduced. An axiomatic framework
and basic properties of RDSIO are developed, and a theorem is shown
that guarantees the stability of interconnected systems.}
}
@INPROCEEDINGS{15cdc_hamadeh_delvecchio,
AUTHOR = {A. O. Hamadeh and E.D. Sontag and Del Vecchio, D.},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Dec. 2015},
TITLE = {A contraction approach to output tracking via high-gain
feedback},
YEAR = {2015},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {7689-7694},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractive systems, contractions,
non-expansive systems},
PDF = {../../FTPDIR/2015cdc_hamadeh_sontag_delvecchio_final_submission_paper_1827.pdf},
ABSTRACT = {This paper adopts a contraction approach to the analysis
of the tracking properties of dynamical systems under high gain
feedback when subject to inputs with bounded derivatives. It is shown
that if the tracking error dynamics are contracting, then the system
is input to output stable with respect to the input signal
derivatives and the output tracking error. As an application, it iss
hown that the negative feedback connection of plants composed of two
strictly positive real LTI subsystems in cascade can follow external
inputs with tracking errors that can be made arbitrarily small by
applying a sufficiently large feedback gain. We utilize this result
to design a biomolecular feedback for a synthetic genetic sensor to
make it robust to variations in the availability of a cellular
resource required for protein production.}
}
@TECHREPORT{biorxiv_change_detection_immune_2015,
AUTHOR = {E.D. Sontag},
INSTITUTION = {bioRxiv http://dx.doi.org/10.1101/035600},
TITLE = {Incoherent feedforward motifs as immune change detectors},
YEAR = {2015},
OPTADDRESS = {},
MONTH = {December},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {scale invariance, fcd, fold change detection, T cells,
incoherent feedforward loops, immunology,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/iffl_immune_change_detectors_biorxiv_035600_30dec2015.pdf},
ABSTRACT = {We speculate that incoherent feedforward loops may be
phenomenologically involved in self/nonself discrimination in
immune-infection and immune-tumor interactions, acting as "change
detectors". In turn, this may result in logarithmic sensing (Weber
phenomenon) and even scale invariance (fold-change detection).}
}
@INCOLLECTION{aminzare_shafi_arcak_sontag_bookchapter2013,
AUTHOR = {Z. Aminzare and Y. Shafi and M. Arcak and E.D. Sontag},
BOOKTITLE = {A Systems Theoretic Approach to Systems and Synthetic Biology I: Models and System Characterizations},
PUBLISHER = {Springer-Verlag},
TITLE = {Guaranteeing spatial uniformity in reaction-diffusion
systems using weighted $L_2$-norm contractions},
YEAR = {2014},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {V. Kulkarni and G.-B. Stan and K. Raman},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {73-101},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, Turing instabilities,
diffusion, partial differential equations, synchronization},
PDF = {../../FTPDIR/aminzare_shafi_arcak_sontag_weighted_L2_contractions_bookchapter2014.pdf},
ABSTRACT = {This paper gives conditions that guarantee spatial
uniformity of the solutions of reaction-diffusion partial
differential equations, stated in terms of the Jacobian matrix and
Neumann eigenvalues of elliptic operators on the given spatial
domain, and similar conditions for diffusively-coupled networks of
ordinary differential equations. Also derived are numerical tests
making use of linear matrix inequalities that are useful in
certifying these conditions.}
}
@ARTICLE{aminzare_sontag_synchronization2014,
AUTHOR = {Z. Aminzare and E.D. Sontag},
JOURNAL = {IEEE Transactions on Network Science and Engineering},
TITLE = {Synchronization of diffusively-connected nonlinear
systems: results based on contractions with respect to general norms},
YEAR = {2014},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {91-106},
VOLUME = {1},
KEYWORDS = {matrix measures, logarithmic norms, synchronization,
consensus, contractions, contractive systems},
PDF = {../../FTPDIR/aminzare_sontag_synchronization_ieee_networks2014.pdf},
ABSTRACT = {Contraction theory provides an elegant way to analyze
the behavior of certain nonlinear dynamical systems. In this paper,
we discuss the application of contraction to synchronization of
diffusively interconnected components described by nonlinear
differential equations. We provide estimates of convergence of the
difference in states between components, in the cases of line,
complete, and star graphs, and Cartesian products of such graphs. We
base our approach on contraction theory, using matrix measures
derived from norms that are not induced by inner products. Such norms
are the most appropriate in many applications, but proofs cannot rely
upon Lyapunov-like linear matrix inequalities, and different
techniques, such as the use of the Perron-Frobenious Theorem in the
cases of L1 or L-infinity norms, must be introduced.}
}
@ARTICLE{enciso_angeli_sontag2014,
AUTHOR = {D. Angeli and G.A. Enciso and E.D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {A small-gain result for orthant-monotone systems under
mixed feedback},
YEAR = {2014},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {9-19},
VOLUME = {68},
KEYWORDS = {small-gain theorem, monotone systems},
PDF = {../../FTPDIR/angeli_enciso_sontag_mixed_feedback_scl2014.pdf},
ABSTRACT = {This paper introduces a small-gain result for
interconnected orthant-monotone systems for which no matching
condition is required between the partial orders in input and output
spaces. Previous results assumed that the partial orders adopted
would be induced by positivity cones in input and output spaces and
that such positivity cones should fulfill a compatibility rule:
namely either be coincident or be opposite. Those two configurations
correspond to positive feedback or negative feedback cases. We relax
those results by allowing arbitrary orthant orders.}
}
@ARTICLE{margaliot_sontag_tuller_ribosome_flow_2013,
AUTHOR = {M. Margaliot and E.D. Sontag and T. Tuller},
JOURNAL = {PLoS ONE},
TITLE = {Entrainment to periodic initiation and transition rates
in a computational model for gene translation},
YEAR = {2014},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {e96039},
VOLUME = {9},
KEYWORDS = {ribosomes, entrainment, nonlinear systems, stability,
contractions, contractive systems, systems biology, RFM,
ribosome flow model},
URL = {http://dx.doi.org/10.1371},
PDF = {../../FTPDIR/margaliot_sontag_tuller_translation_plosone2014_include_grant_correction.pdf},
ABSTRACT = {A recent biological study has demonstrated that the gene
expression pattern entrains to a periodically varying abundance of
tRNA molecules. This motivates developing mathematical tools for
analyzing entrainment of translation elongation to intra-cellular
signals such as tRNAs levels and other factors affecting translation.
We consider a recent deterministic mathematical model for translation
called the Ribosome Flow Model (RFM). We analyze this model under the
assumption that the elongation rate of the tRNA genes and/or the
initiation rate are periodic functions with a common period T. We
show that the protein synthesis pattern indeed converges to a unique
periodic trajectory with period T. The analysis is based on
introducing a novel property of dynamical systems, called contraction
after a short transient (CAST), that may be of independent interest.
We provide a sufficient condition for CAST and use it to prove that
the RFM is CAST, and that this implies entrainment. Our results
support the conjecture that periodic oscillations in tRNA levels and
other factors related to the translation process can induce periodic
oscillations in protein levels, and suggest a new approach for
engineering genes to obtain a desired, periodic, synthesis rate.},
DOI = {10.1371/journal.pone.0096039}
}
@ARTICLE{ambiguity_prabakaran_gunawardena2014,
AUTHOR = {S. Prabakaran and J. Gunawardena and E.D. Sontag},
JOURNAL = {Biophysical Journal},
TITLE = {Paradoxical results in perturbation-based signaling
network reconstruction},
YEAR = {2014},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2720-2728},
VOLUME = {106},
KEYWORDS = {stoichiometry, MAPK cascades, systems biology,
reaction networks, gene and protein networks, reverse engineering,
systems identification, retroactivity},
PDF = {../../FTPDIR/prabakaran_gunawardena_sontag_perturbations_biophysical_journal_2014_reprint_and_supplement.pdf},
ABSTRACT = {This paper describes a potential pitfall of
perturbation-based approaches to network inference It is shows
experimentally, and then explained mathematically, how even in the
simplest signaling systems, perturbation methods may lead to
paradoxical conclusions: for any given pair of two components X and
Y, and depending upon the specific intervention on Y, either an
activation or a repression of X could be inferred. The experiments
are performed in an in vitro minimal system, thus isolating the
effect and showing that it cannot be explained by feedbacks due to
unknown intermediates; this system utilizes proteins from a pathway
in mammalian (and other eukaryotic) cells that play a central role in
proliferation, gene expression, differentiation, mitosis, cell
survival, and apoptosis and is a perturbation target of contemporary
therapies for various types of cancers. The results show that the
simplistic view of intracellular signaling networks being made up of
activation and repression links is seriously misleading, and call for
a fundamental rethinking of signaling network analysis and inference
methods.}
}
@ARTICLE{segall_voigt2014,
AUTHOR = {T.H. Segall-Shapiro and A.J. Meyer and A.D. Ellington and
E.D. Sontag and C.A. Voigt},
JOURNAL = {Molecular Systems Biology},
TITLE = {A `resource allocator' for transcription based on a
highly fragmented T7 RNA polymerase},
YEAR = {2014},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {742-},
VOLUME = {10},
KEYWORDS = {systems biology, synthetic biology, gene expression},
URL = {http://msb.embopress.org/content/10/7/742},
PDF = {../../FTPDIR/segallshapiro_meter_ellington_sontag_voigt_resource_allocator_rna_msb2014.pdf},
ABSTRACT = {A transcriptional system is built based on a 'resource
allocator' that sets a core RNAP concentration, which is then shared
by multiple sigma fragments, which provide specificity. Adjusting the
concentration of the core sets the maximum transcriptional capacity
available to a synthetic system. }
}
@ARTICLE{14iet_sensitivities,
AUTHOR = {E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {A technique for determining the signs of sensitivities
of steady states in chemical reaction networks},
YEAR = {2014},
OPTMONTH = {},
NOTE = {Code is here: https://github.com/sontaglab/CRNSeSi},
OPTNUMBER = {},
PAGES = {251-267},
VOLUME = {8},
KEYWORDS = {sensitivity, retroactivity, biomolecular networks,
systems biology, stoichiometry, reaction networks, systems biology},
PDF = {../../FTPDIR/sensitivities_sontag_iet2014_including_supplement.pdf},
ABSTRACT = { This paper studies the direction of change of steady
states to parameter perturbations in chemical reaction networks, and,
in particular, to changes in conserved quantities. Theoretical
considerations lead to the formulation of a computational procedure
that provides a set of possible signs of such sensitivities. The
procedure is purely algebraic and combinatorial, only using
information on stoichiometry, and is independent of the values of
kinetic constants. Two examples of important intracellular signal
transduction models are worked out as an illustration. In these
examples, the set of signs found is minimal, but there is no general
guarantee that the set found will always be minimal in other
examples. The paper also briefly discusses the relationship of the
sign problem to the question of uniqueness of steady states in
stoichiometry classes. }
}
@INPROCEEDINGS{14cdc_aminzare_tutorial,
AUTHOR = {Z. Aminzare and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
TITLE = {Contraction methods for nonlinear systems: A brief
introduction and some open problems},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3835-3847},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, stability,
reaction-diffusion PDE's, synchronization, contractive systems,
stability},
PDF = {../../FTPDIR/2014_cdc_aminzare_sontag_tutorial_contractions_pp3835_3847_paper2107.pdf},
ABSTRACT = {Contraction theory provides an elegant way to analyze
the behaviors of certain nonlinear dynamical systems. Under sometimes
easy to check hypotheses, systems can be shown to have the
incremental stability property that trajectories converge to each
other. The present paper provides a self-contained introduction to
some of the basic concepts and results in contraction theory,
discusses applications to synchronization and to reaction-diffusion
partial differential equations, and poses several open questions.}
}
@INPROCEEDINGS{14cdc_aminzare,
AUTHOR = {Z. Aminzare and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
TITLE = {Remarks on diffusive-link synchronization using
non-Hilbert logarithmic norms},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {6086-6091},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, stability,
reaction-diffusion PDE's, synchronization},
ABSTRACT = {In this paper, we sketch recent results for
synchronization in a network of identical ODE models which are
diffusively interconnected. In particular, we provide estimates of
convergence of the difference in states between components, in the
cases of line, complete, and star graphs, and Cartesian products of
such graphs.}
}
@INPROCEEDINGS{14cdc_skataric_nikolaev,
AUTHOR = {M. Skataric and E.V. Nikolaev and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
TITLE = {Scale-invariance in singularly perturbed systems},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3035-3040},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
singular perturbations, scale invariance, systems biology,
transient behavior, symmetries, fcd, fold-change detection,
incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/2014_cdc_skataric_nikolaev_sontag_pp3035_3040_paper0094.pdf},
ABSTRACT = {This conference paper (a) summarizes material from "A
fundamental limitation to fold-change detection by biological systems
with multiple time scales" (IET Systems Biology 2014) and presents
additional remarks regarding (b) expansion techniques to compute FCD
error and (c) stochastic adaptation and FCD }
}
@INPROCEEDINGS{skataric_ecc14,
AUTHOR = {M. Skataric and E.D. Sontag},
BOOKTITLE = {Proc. European Control Conference, Strasbourg, France, June 2014},
TITLE = {Remarks on model-based estimation of nonhomogeneous
Poisson processes and applications to biological systems},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2052-2057},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, random dynamical systems},
PDF = {../../FTPDIR/skataric_sontag_nonhomogeneous_markov_ecc2014.pdf},
ABSTRACT = {This paper studies model-based estimation methods of a
rate of a nonhomogeneous Poisson processes that describes events
arising from modeling biological phenomena in which discrete events
are measured. We describe an approach based on observers and Kalman
filters as well as preliminary simulation results, and compare these
to other methods (not model-based) in the literature. The problem is
motivated by the question of identification of internal states from
neural spikes and bacterial tumbling behavior.}
}
@INPROCEEDINGS{14cdc_interconnections,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
TITLE = {Quantifying the effect of interconnections on the steady
states of biomolecular networks},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5419-5424},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{14cdc_margaliot_sontag_tuller_cast,
AUTHOR = {E.D. Sontag and M. Margaliot and T. Tuller},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec. 2014},
TITLE = {On three generalizations of contraction},
YEAR = {2014},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1539-1544},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, stability},
ABSTRACT = {We introduce three forms of generalized
contraction~(GC). Roughly speaking, these are motivated by allowing
contraction to take place after small transients in time and/or
amplitude. Indeed, contraction is usually used to prove asymptotic
properties, like convergence to an attractor or entrainment to a
periodic excitation, and allowing initial transients does not affect
this asymptotic behavior. We provide sufficient conditions for GC,
and demonstrate their usefulness using examples of systems that are
not contractive, with respect to any norm, yet are~GC.}
}
@TECHREPORT{arxiv_barton_sontag_2014,
AUTHOR = {J. Barton and E.D. Sontag},
INSTITUTION = {http://arxiv.org/abs/1412.8065},
TITLE = {Remarks on the energy costs of insulators in enzymatic
cascades},
YEAR = {2014},
OPTADDRESS = {},
MONTH = {December},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
KEYWORDS = {retroactivity, systems biology, reaction networks,
futile cycles, singular perturbations, modularity},
PDF = {../../FTPDIR/barton_sontag_insulators_energy_part2_arxiv2014_1412.8065v1.pdf},
ABSTRACT = { The connection between optimal biological function and
energy use, measured for example by the rate of metabolite
consumption, is a current topic of interest in the systems biology
literature which has been explored in several different contexts. In
[J. P. Barton and E. D. Sontag, Biophys. J. 104, 6 (2013)], we
related the metabolic cost of enzymatic futile cycles with their
capacity to act as insulators which facilitate modular
interconnections in biochemical networks. There we analyzed a simple
model system in which a signal molecule regulates the transcription
of one or more target proteins by interacting with their promoters.
In this note, we consider the case of a protein with an active and an
inactive form, and whose activation is controlled by the signal
molecule. As in the original case, higher rates of energy consumption
are required for better insulator performance.}
}
@INCOLLECTION{angeli_sontag_helmke_volume_2012,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday},
PUBLISHER = {CreateSpace},
TITLE = {Behavior of responses of monotone and sign-definite
systems},
YEAR = {2013},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {K. Hper and Jochen Trumpf},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {51-64},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {monotone systems, reverse engineering, systems biology},
PDF = {../../FTPDIR/angeli_sontag_helmke_volume_2013_reprint.pdf},
ABSTRACT = {This paper study systems with sign-definite interactions
between variables, providing a sufficient condition to characterize
the possible transitions between intervals of increasing and
decreasing behavior. It also provides a discussion illustrating how
our approach can help identify interactions in models, using
information from time series of observations.}
}
@INCOLLECTION{defreitas_sontag_bookchapter2013,
AUTHOR = {de Freitas, M. Marcondes and E.D. Sontag},
BOOKTITLE = {Nonautonomous Dynamical Systems in the Life Sciences, Lecture Notes in Mathematics vol. 2102},
PUBLISHER = {Springer-Verlag},
TITLE = {Random dynamical systems with inputs},
YEAR = {2013},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C. Ptzsche and P. Kloeden},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {41-87},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {random dynamical systems, monotone systems},
PDF = {../../FTPDIR/freitas_bookchapter_2014_reprint.pdf},
ABSTRACT = {This work introduces a notion of random dynamical
systems with inputs, providing several basic definitions and results
on equilibria and convergence. It also presents a "converging input
to converging state" result, a concept that plays a key role in the
analysis of stability of feedback interconnections, for monotone
systems.}
}
@ARTICLE{aminzare_sontag_loglipchitz2012,
AUTHOR = {Z. Aminzare and E.D. Sontag},
JOURNAL = {Nonlinear Analysis: Theory, Methods & Applications},
TITLE = {Logarithmic Lipschitz norms and diffusion-induced
instability},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {31-49},
VOLUME = {83},
KEYWORDS = {contractions, contractive systems, matrix measures,
logarithmic norms, Turing instabilities, diffusion,
partial differential equations, synchronization},
PDF = {../../FTPDIR/aminzare_sontag_contractions_j_nonlinear_analysis_2013.pdf},
ABSTRACT = {This paper proves that ordinary differential equation
systems that are contractive with respect to $L^p$ norms remain so
when diffusion is added. Thus, diffusive instabilities, in the sense
of the Turing phenomenon, cannot arise for such systems, and in fact
any two solutions converge exponentially to each other. The key tools
are semi-inner products and logarithmic Lipschitz constants in Banach
spaces. An example from biochemistry is discussed, which shows the
necessity of considering non-Hilbert spaces. An analogous result for
graph-defined interconnections of systems defined by ordinary
differential equations is given as well.}
}
@ARTICLE{barton_sontag_biophysical_j_2013,
AUTHOR = {J. Barton and E.D. Sontag},
JOURNAL = {Biophysical Journal},
TITLE = {The energy costs of insulators in biochemical networks},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1390-1380},
VOLUME = {104},
KEYWORDS = {reaction networks, futile cycles, enzymatic cycles,
cell signaling, retroactivity, modularity, systems biology},
PDF = {../../FTPDIR/barton_sontag_retroactivity_energy_biophysical_journal2013.pdf},
ABSTRACT = {Complex networks of biochemical reactions, such as
intracellular protein signaling pathways and genetic networks, are
often conceptualized in terms of ``modules,'' semi-independent
collections of components that perform a well-defined function and
which may be incorporated in multiple pathways. However, due to
sequestration of molecular messengers during interactions and other
effects, collectively referred to as retroactivity, real biochemical
systems do not exhibit perfect modularity. Biochemical signaling
pathways can be insulated from impedance and competition effects,
which inhibit modularity, through enzymatic ``futile cycles'' which
consume energy, typically in the form of ATP. We hypothesize that
better insulation necessarily requires higher energy consumption. We
test this hypothesis through a combined theoretical and computational
analysis of a simplified physical model of covalent cycles, using two
innovative measures of insulation, as well as a new way to
characterize optimal insulation through the balancing of these two
measures in a Pareto sense. Our results indicate that indeed better
insulation requires more energy. While insulation may facilitate
evolution by enabling a modular ``plug and play'' interconnection
architecture, allowing for the creation of new behaviors by adding
targets to existing pathways, our work suggests that this potential
benefit must be balanced against the metabolic costs of insulation
necessarily incurred in not affecting the behavior of existing
processes.}
}
@ARTICLE{hamadeh_ingalls_sontag_2012,
AUTHOR = {A.O. Hamadeh and B.P. Ingalls and E.D. Sontag},
JOURNAL = {Proc. Royal Society Interface},
TITLE = {Transient dynamic phenotypes as criteria for model
discrimination: fold-change detection in Rhodobacter sphaeroides
chemotaxis},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {20120935},
VOLUME = {10},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, chemotaxis},
PDF = {../../FTPDIR/hamadeh_ingalls_sontag_royal_society_interface_2013_reprint.pdf},
ABSTRACT = {The chemotaxis pathway of the bacterium Rhodobacter
sphaeroides has many similarities to that of Escherichia coli. It
exhibits robust adaptation and has several homologues of the latter's
chemotaxis proteins. Recent theoretical results have correctly
predicted that, in response to a scaling of its ligand input signal,
Escherichia coli exhibits the same output behavior, a property known
as fold-change detection (FCD). In light of recent experimental
results suggesting that R. sphaeroides may also show FCD, we present
theoretical assumptions on the R. sphaeroides chemosensory dynamics
that can be shown to yield FCD behavior. Furthermore, it is shown
that these assumptions make FCD a property of this system that is
robust to structural and parametric variations in the chemotaxis
pathway, in agreement with experimental results. We construct and
examine models of the full chemotaxis pathway that satisfy these
assumptions and reproduce experimental time-series data from earlier
studies. We then propose experiments in which models satisfying our
theoretical assumptions predict robust FCD behavior where earlier
models do not. In this way, we illustrate how transient dynamic
phenotypes such as FCD can be used for the purposes of discriminating
between models that reproduce the same experimental time-series data.}
}
@ARTICLE{blerisreverse2013,
AUTHOR = {T. Kang and J.T. White and Z. Xie and Y. Benenson and
E.D. Sontag and L. Bleris},
JOURNAL = {ACS Synthetic Biology},
TITLE = {Reverse engineering validation using a benchmark
synthetic gene circuit in human cells},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {255-262},
VOLUME = {2},
KEYWORDS = {reverse engineering, systems biology, synthetic biology},
PDF = {../../FTPDIR/kang_white_xie_benenson_sontag_bleris_reverse-engineering_acs2013.pdf},
ABSTRACT = {This work introduces an experimental platform customized
for the development and verification of reverse engineering and
pathway characterization algorithms in mammalian cells. Specifically,
we stably integrate a synthetic gene network in human kidney cells
and use it as a benchmark for validating reverse engineering
methodologies. The network, which is orthogonal to endogenous
cellular signaling, contains a small set of regulatory interactions
that can be used to quantify the reconstruction performance. By
performing successive perturbations to each modular component of the
network and comparing protein and RNA measurements, we study the
conditions under which we can reliably reconstruct the causal
relationships of the integrated synthetic network.}
}
@ARTICLE{liu_et_al_austin_pnas2013,
AUTHOR = {L. Liu and G. Duclos and B. Sun and J. Lee and A. Wu and
Y. Kam and E.D. Sontag and H.A. Stone and J.C. Sturm and R.A. Gatenby and
R.H. Austin},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Minimization of thermodynamic costs in cancer cell
invasion},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1686-1691},
VOLUME = {110},
KEYWORDS = {chemotaxis, cancer, metastasis},
PDF = {../../FTPDIR/liu_et_al_austin_cancer_metastasis_pnas2013.pdf},
ABSTRACT = {This paper shows that metastatic breast cancer cells
cooperatively invade a 3D collagen matrix while following a glucose
gradient. The front cell leadership is dynamic, and invading cells
act in a cooperative manner by exchanging leaders in the invading
front.}
}
@ARTICLE{russo_dibernardo_sontag11,
AUTHOR = {G. Russo and di Bernardo, M. and E.D. Sontag},
JOURNAL = {IEEE Transactions Autom. Control},
TITLE = {A contraction approach to the hierarchical analysis and
design of networked systems},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1328-1331},
VOLUME = {58},
KEYWORDS = {contractions, contractive systems, matrix measures,
logarithmic norms, synchronization, systems biology},
PDF = {../../FTPDIR/russo_dibernardo_sontag_hierarchical_contractions_ieee2013.pdf},
ABSTRACT = {This paper studies networks of components, and shows
that a contraction property on the interconnection matrix, coupled
with contractivity of the individual component subsystems, suffices
to insure contractivity of the overall system. }
}
@ARTICLE{blerisnoise2013,
AUTHOR = {V. Shimoga and J.T. White and Y. Li and E.D. Sontag and
L. Bleris},
JOURNAL = {Molecular Systems Biology},
TITLE = {Synthetic mammalian transgene negative autoregulation},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {670-},
VOLUME = {9},
KEYWORDS = {systems biology, synthetic biology, gene expression},
PDF = {../../FTPDIR/shimoga_white_li_sontag_bleris_msb2013.pdf},
ABSTRACT = {Using synthetic circuits stably integrated in human
kidney cells, we study the effect of negative feedback regulation on
cell-wide (extrinsic) and gene-specific (intrinsic) sources of
uncertainty. We develop a theoretical approach to extract the two
noise components from experiments and show that negative feedback
reduces extrinsic noise while marginally increasing intrinsic noise,
resulting to significant total noise reduction. We compare the
results to simple negative regulation, where a constitutively
transcribed transcription factor represses a reporter protein. We
observe that the control architecture also reduces the extrinsic
noise but results in substantially higher intrinsic fluctuations. We
conclude that negative feedback is the most efficient way to mitigate
the effects of extrinsic fluctuations by a sole regulatory wiring.}
}
@ARTICLE{white2013journal,
AUTHOR = {A. White and B. Lees and H.-L. Kao and G. Cipriani and
E. Munarriz and A. Paaby and K. Erickson and S. Guzman and
K. Rattanakorn and E.D. Sontag and D. Geiger and K. Gunsalus and
F. Piano},
JOURNAL = {IEEE Transactions on Medical Imaging},
TITLE = {DevStaR: A novel algorithm for quantitative phenotyping
of C. elegans development},
YEAR = {2013},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1791-1803},
VOLUME = {32},
PDF = {../../FTPDIR/white_et_al_devstar_ieee_trans_medical_imaging_32_2013_pp_1791_1803.pdf}
}
@INPROCEEDINGS{hamadehacc2013,
AUTHOR = {A. O. Hamadeh and E.D. Sontag and B.P. Ingalls},
BOOKTITLE = {Proc. American Control Conference},
TITLE = {Response time re-scaling and Weber's law in adapting
biological systems},
YEAR = {2013},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4564-4569},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, chemotaxis},
PDF = {../../FTPDIR/hamadeh_sontag_ingalls_2013acc.pdf},
ABSTRACT = {Recent experimental work has shown that transient E.
coli chemotactic response is unchanged by a scaling of its ligand
input signal (fold change detection, or FCD), and this is in
agreement with earlier mathematical predictions. However, this
prediction was based on certain particular assumptions on the
structure of the chemotaxis pathway. In this work, we begin by
showing that behavior similar to FCD can be obtained under weaker
conditions on the system structure. Namely, we show that under
relaxed conditions, a scaling of the chemotaxis system's inputs leads
to a time scaling of the output response. We propose that this may be
a contributing factor to the robustness of the experimentally
observed FCD. We further show that FCD is a special case of this time
scaling behavior for which the time scaling factor is unity. We then
proceed to extend the conditions for output time scaling to more
general adapting systems, and demonstrate this time scaling behavior
on a published model of the chemotaxis pathway of the bacterium
Rhodobacter sphaeroides. This work therefore provides examples of how
robust biological behavior can arise from simple yet realistic
conditions on the underlying system structure.}
}
@INPROCEEDINGS{shafi_aminzare_arcak_sontag_acc2013,
AUTHOR = {Y. Shafi and Z. Aminzare and M. Arcak and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conference},
TITLE = {Spatial uniformity in diffusively-coupled systems using
weighted L2 norm contractions},
YEAR = {2013},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5639-5644},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, matrix measures,
logarithmic norms, Turing instabilities, diffusion,
partial differential equations, synchronization},
PDF = {../../FTPDIR/shafi_aminzare_arcak_sontag_2013acc.pdf},
ABSTRACT = {We present conditions that guarantee spatial uniformity
in diffusively-coupled systems. Diffusive coupling is a ubiquitous
form of local interaction, arising in diverse areas including
multiagent coordination and pattern formation in biochemical
networks. The conditions we derive make use of the Jacobian matrix
and Neumann eigenvalues of elliptic operators, and generalize and
unify existing theory about asymptotic convergence of trajectories of
reaction-diffusion partial differential equations as well as
compartmental ordinary differential equations. We present numerical
tests making use of linear matrix inequalities that may be used to
certify these conditions. We discuss an example pertaining to
electromechanical oscillators. The paper's main contributions are
unified verifiable relaxed conditions that guarantee synchrony.}
}
@INPROCEEDINGS{freitasacc2013,
AUTHOR = {de Freitas, M. Marcondes and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conference},
TITLE = {A class of random control systems: Monotonicity and the
convergent-input convergent-state property},
YEAR = {2013},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4564-4569},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {random dynamical systems, monotone systems},
PDF = {../../FTPDIR/freitas_sontag_2013acc.pdf}
}
@TECHREPORT{arxiv_aminzare_sontag_chemotaxis_advection_diffusion_feb2013,
AUTHOR = {Z. Aminzare and E. D. Sontag},
INSTITUTION = {arxiv:1302.2605},
TITLE = {Remarks on a population-level model of chemotaxis:
advection-diffusion approximation and simulations},
YEAR = {2013},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
PDF = {http://arxiv.org/pdf/1302.2605},
ABSTRACT = {This note works out an advection-diffusion approximation
to the density of a population of E. coli bacteria undergoing
chemotaxis in a one-dimensional space. Simulations show the high
quality of predictions under a shallow-gradient regime.}
}
@TECHREPORT{arxiv_polynomials_2013,
AUTHOR = {E.D. Sontag},
INSTITUTION = {arxiv 1302.0759},
TITLE = {A remark about polynomials with specified local minima
and no other critical points},
YEAR = {2013},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
PDF = {http://arxiv.org/pdf/1302.0759},
ABSTRACT = {The following observation must surely be "well-known",
but it seems worth giving a simple and quite explicit proof. Take any
finite subset X of Rn, n>1. Then, there is a polynomial function P:Rn
-> R which has local minima on the set X, and has no other critical
points. Applied to the negative gradient flow of P, this implies that
there is a polynomial vector field with asymptotically stable
equilibria on X and no other equilibria. Some trajectories of this
vector field are not pre-compact; a complementary observation says
that, again for arbitrary X, one can find a vector field with
asymptotically stable equilibria on X, no other equilibria except
saddles, and all omega-limit sets consisting of singletons.}
}
@ARTICLE{weiss12homeostasis,
AUTHOR = {M. Miller and M. Hafner and E.D. Sontag and N. Davidsohn and
S. Subramanian and P. E. M. Purnick and D. Lauffenburger and R. Weiss},
JOURNAL = {PLoS Computational Biology},
TITLE = {Modular design of artificial tissue homeostasis: robust
control through synthetic cellular heterogeneity},
YEAR = {2012},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1002579-},
VOLUME = {8},
KEYWORDS = {systems biology, homeostasis, stem cells,
synthetic biology},
PDF = {../../FTPDIR/miller_hafner_sontag_et_al_weiss_plos2012_all_files.pdf},
ABSTRACT = {Synthetic biology efforts have largely focused on small
engineered gene networks, yet understanding how to integrate multiple
synthetic modules and interface them with endogenous pathways remains
a challenge. Here we present the design, system integration, and
analysis of several large scale synthetic gene circuits for
artificial tissue homeostasis. Diabetes therapy represents a possible
application for engineered homeostasis, where genetically programmed
stem cells maintain a steady population of beta-cells despite
continuous turnover. We develop a new iterative process that
incorporates modular design principles with hierarchical performance
optimization targeted for environments with uncertainty and
incomplete information. We employ theoretical analysis and
computational simulations of multicellular reaction/diffusion models
to design and understand system behavior, and find that certain
features often associated with robustness (e.g., multicellular
synchronization and noise attenuation) are actually detrimental for
tissue homeostasis. We overcome these problems by engineering a new
class of genetic modules for 'synthetic cellular heterogeneity' that
function to generate beneficial population diversity. We design two
such modules (an asynchronous genetic oscillator and a signaling
throttle mechanism), demonstrate their capacity for enhancing robust
control, and provide guidance for experimental implementation with
various computational techniques. We found that designing modules for
synthetic heterogeneity can be complex, and in general requires a
framework for non-linear and multifactorial analysis. Consequently,
we adapt a 'phenotypic sensitivity analysis' method to determine how
functional module behaviors combine to achieve optimal system
performance. We ultimately combine this analysis with Bayesian
network inference to extract critical, causal relationships between a
module's biochemical rate-constants, its high level functional
behavior in isolation, and its impact on overall system performance
once integrated.}
}
@ARTICLE{12automatica_rufinoferreira_arcak_sontag,
AUTHOR = {Rufino Ferreira, A. and M. Arcak and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Stability certification of large scale stochastic
systems using dissipativity of subsystems},
YEAR = {2012},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {2956-2964},
VOLUME = {48},
KEYWORDS = {stochastic systems, passivity, noise-to-state stability,
ISS, input to state stability},
PDF = {../../FTPDIR/rufinoferreira_arcak_sontag_automatica2012.pdf},
ABSTRACT = {This paper deals with the stability of interconnections
of nonlinear stochastic systems, using concepts of passivity and
noise-to-state stability.}
}
@ARTICLE{12skataric_fcd,
AUTHOR = {M. Skataric and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {A characterization of scale invariant responses in
enzymatic networks},
YEAR = {2012},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1002748},
VOLUME = {8},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection},
PDF = {../../FTPDIR/skataric_sontag_plos2012_reprint_and_supplement.pdf},
ABSTRACT = {This paper studies a recently discovered remarkable
feature that was shown in many adapting systems: scale invariance,
which means that the initial, transient behavior stays approximately
the same when the background signal level is scaled. Not every
adapting system is scale-invariant: we investigate under which
conditions a broadly used model of biochemical enzymatic networks
will show scale invariant behavior. For all 3-node enzymatic
networks, we performed a wide computational study to find candidates
for scale invariance, among 16,038 possible topologies. This effort
led us to discover a new necessary and sufficient mechanism that
explains the behavior of all 3-node enzyme networks that have this
property, which we call``uniform linearizations with fast output''.
We also apply our theoretical results to a concrete biological
example of order six, a model of the response of the chemotaxis
signaling pathway of Dictyostelium discoideum to changes in
chemoeffector cyclic adenosine monophosphate (cAMP).}
}
@ARTICLE{wood_et_al_2012,
AUTHOR = {K. Wood and S. Nishida and E.D. Sontag and P. Cluzel},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Mechanism-independent method for predicting response to
multiple drug exposure in bacteria},
YEAR = {2012},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {12254-12259},
VOLUME = {109},
KEYWORDS = {systems biology, drug interactions},
PDF = {../../FTPDIR/wood_nishida_sontag_cluzel_pnas2012_all_files.pdf},
ABSTRACT = {Drugs are commonly used in combinations larger than two
for treating bacterial infections. It is generally impossible to
infer directly from the effects of individual drugs the net effect of
a multi-drug combination. This paper describes an empirically derived
mechanism-independent method for predicting the microbial growth
response to combinations of more than two drugs, experimentally
tested on both gram-negative (Escherichia coli) and grampositive
(Staphylococcus aureus) bacteria. The method shows that for a wide
range of drugs, the bacterial responses to drug pairs are sufficient
to infer the effects of larger drug combinations, and provides a
simple formula for the prediction.}
}
@INPROCEEDINGS{12cdc_angeli_sontag,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012},
TITLE = {Remarks on the invalidation of biological models using
monotone systems theory},
YEAR = {2012},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Paper TuC09.3.},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/12cdc_angeli_sontag_monotone_behaviors_final_version_28aug2012.pdf},
ABSTRACT = {This paper presents techniques for finding out what type
of solutions are compatible with a given sign pattern of interactions
between state/input variables once the input behaviour is also known.
By ``type'' of solutions we essentially refer to the sequence of
upwards or downwards segments that variables can exhibit (essentially
sign-patterns of variables derivatives) once input profiles are also
specified. A concrete experimental example of how such techniques can
invalidate models is also provided.}
}
@INPROCEEDINGS{12cdc_hamadeh,
AUTHOR = {A.O. Hamadeh and B.P. Ingalls and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012},
TITLE = {Fold-Change Detection As a Chemotaxis Model
Discrimination Tool},
YEAR = {2012},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Paper WeC09.2.},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, chemotaxis}
}
@INPROCEEDINGS{12acc_arcak,
AUTHOR = {Rufino Ferreira, A. and M. Arcak and E.D. Sontag},
BOOKTITLE = {Proceedings of the 2012 American Control Conference, Montreal, June 2012},
TITLE = {A decomposition-based approach to stability analysis of
large-scale stochastic systems},
YEAR = {2012},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {Paper FrC10.4},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {stochastic systems, passivity, noise-to-state stability},
ABSTRACT = {Conference version of ``Stability certification of large
scale stochastic systems using dissipativity of subsystems''.}
}
@INPROCEEDINGS{12cdc_skataric_sontag,
AUTHOR = {M. Skataric and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2012},
TITLE = {Exploring the scale invariance property in enzymatic
networks},
YEAR = {2012},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Paper WeC09.2.},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, enzymatic networks},
ABSTRACT = {This is a conference version of ``A characterization of
scale invariant responses in enzymatic networks.}
}
@INCOLLECTION{craciun_book10,
AUTHOR = {G. Craciun and C. Pantea and E.D. Sontag},
BOOKTITLE = {Design and Analysis of Biomolecular Circuits},
PUBLISHER = {Springer-Verlag},
TITLE = {Graph-theoretic analysis of multistability and
monotonicity for biochemical reaction networks},
YEAR = {2011},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {H. Koeppl and G. Setti and di Bernardo, M. and
D. Densmore},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {63-72},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {reaction networks, monotone systems},
PDF = {../../FTPDIR/pantea_sontag_graph_theoretic_bookchapter2011.pdf},
ABSTRACT = {This is a short expository article describing how the
species-reaction graph (SR graph) can be used to analyze both
multistability and monotonicity of biochemical networks.}
}
@INCOLLECTION{ControlHandbook2ed_sontag_ISS,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {The Control Systems Handbook: Control System Advanced Methods, Second Edition.},
PUBLISHER = {CRC Press, Boca Raton},
TITLE = {Input to State Stability},
YEAR = {2011},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {W. S. Levine},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {45.1-45.21 (1034-1054)},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
input to output stability},
PDF = {../../FTPDIR/sontag_iss_handbook_second_edition_2011.pdf},
ABSTRACT = { An encyclopedia-type article on foundations of ISS. }
}
@INCOLLECTION{mra_book10,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Design and Analysis of Biomolecular Circuits},
PUBLISHER = {Springer-Verlag},
TITLE = {Modularity, retroactivity, and structural identification},
YEAR = {2011},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {H. Koeppl and G. Setti and di Bernardo, M. and
D. Densmore},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {183-202},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {modularity, retroactivity, identification},
PDF = {../../FTPDIR/mra_koeppel_book2011_published.pdf},
ABSTRACT = {Many reverse-engineering techniques in systems biology
rely upon data on steady-state (or dynamic) perturbations --obtained
from siRNA, gene knock-down or overexpression, kinase and phosphatase
inhibitors, or other interventions-- in order to understand the
interactions between different ``modules'' in a network. This paper
first reviews one such popular such technique, introduced by the
author and collaborators, and focuses on why conclusions drawn from
its use may be misleading due to ``retroactivity'' (impedance or
load) effects. A theoretical result characterizing
stoichiometric-induced steady-state retroactivity effects is given
for a class of biochemical networks.}
}
@INCOLLECTION{stabilization_encyclopaedia13,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Mathematics of Complexity and Dynamical Systems},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {Stability and feedback stabilization},
YEAR = {2011},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {Robert Meyers},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1639-1652},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {stability, nonlinear control, feedback stabilization},
PDF = {../../FTPDIR/stability_feedback_stabilization_encyclopedia_complexity_systems_science_sontag_2013.pdf},
ABSTRACT = {The problem of stabilization of equilibria is one of the
central issues in control. In addition to its intrinsic interest, it
represents a first step towards the solution of more complicated
problems, such as the stabilization of periodic orbits or general
invariant sets, or the attainment of other control objectives, such
as tracking, disturbance rejection, or output feedback, all of which
may be interpreted as requiring the stabilization of some quantity
(typically, some sort of ``error'' signal). A very special case, when
there are no inputs, is that of stability. This short and informal
article provides an introduction to the subject. }
}
@INCOLLECTION{ControlHandbook2ed_teel_georgiou_praly_sontag,
AUTHOR = {A.R. Teel and T.T. Georgiou and L. Praly and E.D. Sontag},
BOOKTITLE = {The Control Systems Handbook: Control System Advanced Methods, Second Edition.},
PUBLISHER = {CRC Press, Boca Raton},
TITLE = {Input-Output Stability},
YEAR = {2011},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {W. S. Levine},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {44.1-44.23 (1011-1033)},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/teel_georgiou_praly_sontag_io_stability_handbook_second_edition_2011.pdf},
ABSTRACT = { An encyclopedia-type article on foundations of
input/output stability. }
}
@ARTICLE{dasgupta_redundancy2011,
AUTHOR = {R. Albert and B. DasGupta and R. Hegde and
G.S. Sivanathan and A. Gitter and G. Grsoy and P. Paul and
E.D. Sontag},
JOURNAL = {Physical Review E},
TITLE = {A new computationally efficient measure of topological
redundancy of biological and social networks},
YEAR = {2011},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {036117},
VOLUME = {84},
PDF = {../../FTPDIR/albert_dasgupta_sontag_phyrevE_2011.pdf},
ABSTRACT = {In this paper, we introduce a topological redundancy
measure for labeled directed networks that is formal, computationally
efficient and applicable to a variety of directed networks such as
cellular signaling, metabolic and social interaction networks. We
demonstrate the computational efficiency of our measure by computing
its value and statistical significance on a number of biological and
social networks with up to several thousands of nodes and edges. Our
results suggest a number of interesting observations: (1) social
networks are more redundant that their biological counterparts, (2)
transcriptional networks are less redundant than signaling networks,
(3) the topological redundancy of the C. elegans metabolic network is
largely due to its inclusion of currency metabolites, and (4) the
redundancy of signaling networks is highly (negatively) correlated
with monotonicity of their dynamics.}
}
@ARTICLE{timevarying_persistence_angeli_leenheer,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
JOURNAL = {SIAM Journal on Applied Mathematics},
TITLE = {Persistence results for chemical reaction networks with
time-dependent kinetics and no global conservation laws},
YEAR = {2011},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {128-146},
VOLUME = {71},
KEYWORDS = {reaction networks, fluxes, Petri nets, persistence,
reaction networks with inputs},
PDF = {../../FTPDIR/angeli_leenheer_sontag_siap_online2011.pdf},
ABSTRACT = {New checkable criteria for persistence of chemical
reaction networks are proposed, which extend and complement existing
ones. The new results allow the consideration of reaction rates which
are time-varying, thus incorporating the effects of external signals,
and also relax the assumption of existence of global conservation
laws, thus allowing for inflows (production) and outflows
(degradation). For time-invariant networks parameter-dependent
conditions for persistence of certain classes of networks are
provided. As an illustration, two networks arising in the systems
biology literature are analyzed, namely a hypoxia and an apoptosis
network. }
}
@ARTICLE{bleris10,
AUTHOR = {L. Bleris and Z. Xie and D. Glass and A. Adadey and
E.D. Sontag and Y. Benenson},
JOURNAL = {Molecular Systems Biology},
TITLE = {Synthetic incoherent feed-forward circuits show
adaptation to the amount of their genetic template},
YEAR = {2011},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {519-},
VOLUME = {7},
KEYWORDS = {adaptation, feedforward loops, systems biology,
synthetic biology, incoherent feedforward loop, feedforward, IFFL},
PDF = {../../FTPDIR/bleris_xie_glass_adadey_sontag_benenson_molsysbio2011.pdf},
ABSTRACT = {Natural and synthetic biological networks must function
reliably in the face of fluctuating stoichiometry of their molecular
components. These fluctuations are caused in part by changes in
relative expression efficiency and the DNA template amount of the
network-coding genes. Gene product levels could potentially be
decoupled from these changes via built-in adaptation mechanisms,
thereby boosting network reliability. Here we show that a mechanism
based on an incoherent feed-forward motif enables adaptive gene
expression in mammalian cells. We modeled, synthesized, and tested
transcriptional and post-transcriptional incoherent loops and found
that in all cases the gene product adapts to changes in DNA template
abundance. We also observed that the post-transcriptional form
results in superior adaptation behavior, higher absolute expression
levels, and lower intrinsic fluctuations. Our results support a
previously-hypothesized endogenous role in gene dosage compensation
for such motifs and suggest that their incorporation in synthetic
networks will improve their robustness and reliability.}
}
@ARTICLE{Dashkovskiy-Efimov-Sontag-11,
AUTHOR = {S.N. Dashkovskiy and D.V. Efimov and E.D. Sontag},
JOURNAL = {Avtomatika i Telemekhanika (Automation and Remote Control)},
TITLE = {Ustoichivost' ot vhoda k sostoyaniu i smezhnie svoystva
sistem (In Russian, Input to state stability and allied system
properties)},
YEAR = {2011},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {8},
PAGES = {1579-1614},
VOLUME = {72},
PDF = {../../FTPDIR/dashkovskiy_efimov_sontag_automation_remote_control2011_russian.pdf}
}
@ARTICLE{ddv11,
AUTHOR = {A.C. Jiang and A. C. Ventura and E. D. Sontag and
S. D. Merajver and A. J. Ninfa and Del Vecchio, D.},
JOURNAL = {Science Signaling},
TITLE = {Load-induced modulation of signal transduction networks},
YEAR = {2011},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {ra67},
VOLUME = {4, issue 194},
KEYWORDS = {systems biology, reaction networks, synthetic biology,
futile cycles, singular perturbations, modularity},
PDF = {../../FTPDIR/delvecchio_etc_science_signaling2011.pdf},
ABSTRACT = {Biological signal transduction networks are commonly
viewed as circuits that pass along in the process amplifying signals,
enhancing sensitivity, or performing other signal-processing to
transcriptional and other components. Here, we report on a
"reverse-causality" phenomenon, which we call load-induced
modulation. Through a combination of analytical and experimental
tools, we discovered that signaling was modulated, in a surprising
way, by downstream targets that receive the signal and, in doing so,
apply what in physics is called a load. Specifically, we found that
non-intuitive changes in response dynamics occurred for a covalent
modification cycle when load was present. Loading altered the
response time of a system, depending on whether the activity of one
of the enzymes was maximal and the other was operating at its minimal
rate or whether both enzymes were operating at submaximal rates.
These two conditions, which we call "limit regime" and "intermediate
regime," were associated with increased or decreased response times,
respectively. The bandwidth, the range of frequency in which the
system can process information, decreased in the presence of load,
suggesting that downstream targets participate in establishing a
balance between noise-filtering capabilities and a its ability to
process high-frequency stimulation. Nodes in a signaling network are
not independent relay devices, but rather are modulated by their
downstream targets}
}
@ARTICLE{shoval_alon_sontag_2011,
AUTHOR = {O. Shoval and U. Alon and E.D. Sontag},
JOURNAL = {SIAM Journal on Applied Dynamical Systems},
TITLE = {Symmetry invariance for adapting biological systems},
YEAR = {2011},
OPTMONTH = {},
NOTE = {(See here for a small typo: http://www.sontaglab.org/FTPDIR/shoval.alon.sontag.erratum.pdf)},
OPTNUMBER = {},
PAGES = {857-886},
VOLUME = {10},
KEYWORDS = {identifiability, adaptation, biological adaptation,
perfect adaptation, adaptation, feedforward loops, integral feedback,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, incoherent feedforward loop, feedforward,
IFFL},
PDF = {../../FTPDIR/shoval_alon_sontag_siads2011.pdf},
ABSTRACT = {Often, the ultimate goal of regulation is to maintain a
narrow range of concentration levels of vital quantities
(homeostasis, adaptation) while at the same time appropriately
reacting to changes in the environment (signal detection or
sensitivity). Much theoretical, modeling, and analysis effort has
been devoted to the understanding of these questions, traditionally
in the context of steady-state responses to constant or step-changing
stimuli. In this paper, we present a new theorem that provides a
necessary and sufficient characterization of invariance of transient
responses to symmetries in inputs. A particular example of this
property, scale invariance (a.k.a. "fold change detection"), appears
to be exhibited by biological sensory systems ranging from bacterial
chemotaxis pathways to signal transduction mechanisms in eukaryotes.
The new characterization amounts to the solvability of an associated
partial differential equation. It is framed in terms of a notion
which considerably extends equivariant actions of compact Lie groups.
For several simple system motifs that are recurrent in biology, the
solvability criterion may be checked explicitly.}
}
@INPROCEEDINGS{11cdc_angeli,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2011},
TITLE = {A small-gain result for orthant-monotone systems in
feedback: the non sign-definite case},
YEAR = {2011},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {WeC09.1},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {small-gain theorem, monotone systems},
ABSTRACT = {This note introduces a small-gain result for
interconnected MIMO orthant-monotone systems for which no matching
condition is required between the partial orders in input and output
spaces of the considered subsystems. Previous results assumed that
the partial orders adopted would be induced by positivity cones in
input and output spaces and that such positivity cones should fulfill
a compatibility rule: namely either be coincident or be opposite.
Those two configurations corresponded to positive-feedback or
negative feedback cases. We relax those results by allowing arbitrary
orthant orders.}
}
@INPROCEEDINGS{11cdc_shoval_alon_sontag,
AUTHOR = {O. Shoval and U. Alon and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2011},
TITLE = {Input symmetry invariance, and applications to
biological systems},
YEAR = {2011},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {TuA02.5},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
adaptation, feedforward loops, integral feedback, scale invariance,
systems biology, transient behavior, symmetries, fcd,
fold-change detection, jump Markov processes},
ABSTRACT = {This paper studies invariance with respect to symmetries
in sensory fields, a particular case of which, scale invariance, has
recently been found in certain eukaryotic as well as bacterial cell
signaling systems. We describe a necessary and sufficient
characterization of symmetry invariance in terms of equivariant
transformations, show how this characterization helps find all
possible symmetries in standard models of biological adaptation, and
discuss symmetry-invariant searches.}
}
@MISC{fcd_pde_arxiv_aug2011,
AUTHOR = {E.D. Sontag},
OPTHOWPUBLISHED = {},
OPTMONTH = {},
OPTNOTE = {},
TITLE = {Remarks on invariance of population distributions for
systems with equivariant internal dynamics},
YEAR = {2011},
KEYWORDS = {adaptation, biological adaptation, perfect adaptation,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, jump Markov processes},
URL = {https://doi.org/10.48550/arXiv.1108.3245},
PDF = {../../FTPDIR/fcd_pde_arxiv_aug2011.pdf}
}
@INCOLLECTION{albert-dasgupta-sontag-inference2010,
AUTHOR = {R. Albert and B. Dasgupta and E.D. Sontag},
BOOKTITLE = {Computational Biology, Methods in Molecular Biology vol. 673},
PUBLISHER = {Springer},
TITLE = {Inference of signal transduction networks from double
causal evidence},
YEAR = {2010},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {David Feny},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {239-251},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, algorithms,
signal transduction networks, graph algorithms},
PDF = {../../FTPDIR/albert_dasgupta_sontag_inference_signal_transduction.pdf},
ABSTRACT = {We present a novel computational method, and related
software, to synthesize signal transduction networks from single and
double causal evidence.}
}
@INCOLLECTION{DasguptaVeraLiconaSontag2010,
AUTHOR = {B. Dasgupta and P. Vera-Licona and E.D. Sontag},
BOOKTITLE = {Algorithms in computational molecular biology: Techniques, Approaches and Applications},
PUBLISHER = {Wiley},
TITLE = {Reverse engineering of molecular networks from a common
combinatorial approach},
YEAR = {2010},
ADDRESS = {Hoboken},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {M. Elloumi and A.Y. Zomaya},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {941-954},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {reverse engineering, systems biology},
PDF = {../../FTPDIR/dasgupta_veralicona_sontag_reverse_engineering_algorithms_comp_molbio2011.pdf}
}
@INCOLLECTION{sontag10yamamoto,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Perspectives in Mathematical System Theory, Control, and Signal Processing},
PUBLISHER = {Springer-verlag},
TITLE = {Contractive systems with inputs},
YEAR = {2010},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {Jan Willems and Shinji Hara and Yoshito Ohta and
Hisaya Fujioka},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {217-228},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {contractions, contractive systems, consensus,
synchronization},
PDF = {../../FTPDIR/sontag10yamamoto.pdf},
ABSTRACT = {Contraction theory provides an elegant way of analyzing
the behaviors of systems subject to external inputs. Under sometimes
easy to check hypotheses, systems can be shown to have the
incremental stability property that all trajectories converge to a
unique solution. This property is especially interesting when forcing
functions are periodic (globally attracting limit cycles result), as
well as in the context of establishing synchronization results. The
present paper provides a self-contained introduction to some basic
results, with a focus on contractions with respect to non-Euclidean
metrics.}
}
@ARTICLE{reaction_coordinates08,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
JOURNAL = {J. Mathematical Biology},
TITLE = {Graph-theoretic characterizations of monotonicity of
chemical networks in reaction coordinates},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {581-616},
VOLUME = {61},
KEYWORDS = {MAPK cascades, reaction networks, fluxes,
monotone systems, reaction cordinates, Petri nets, persistence,
futile cycles},
PDF = {../../FTPDIR/angeli_leenheer_sontag_graphs_JMB2010.pdf},
ABSTRACT = { This paper derives new results for certain classes of
chemical reaction networks, linking structural to dynamical
properties. In particular, it investigates their monotonicity and
convergence without making assumptions on the form of the kinetics
(e.g., mass-action) of the dynamical equations involved, and relying
only on stoichiometric constraints. The key idea is to find an
alternative representation under which the resulting system is
monotone. As a simple example, the paper shows that a
phosphorylation/dephosphorylation process, which is involved in many
signaling cascades, has a global stability property. }
}
@ARTICLE{russo_dibernardo_sontag09,
AUTHOR = {G. Russo and di Bernardo, M. and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Global entrainment of transcriptional systems to
periodic inputs},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e1000739},
VOLUME = {6},
KEYWORDS = {contractive systems, contractions, systems biology,
reaction networks, gene and protein networks},
PDF = {../../FTPDIR/russo_dibernardo_sontag_entrainment_plos2010.pdf},
ABSTRACT = {This paper addresses the problem of giving conditions
for transcriptional systems to be globally entrained to external
periodic inputs. By using contraction theory, a powerful tool from
dynamical systems theory, it is shown that certain systems driven by
external periodic signals have the property that all solutions
converge to fixed limit cycles. General results are proved, and the
properties are verified in the specific case of some models of
transcriptional systems. }
}
@ARTICLE{scardovi_arcak_TAC09,
AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag},
JOURNAL = {IEEE Transactions Autom. Control},
TITLE = {Synchronization of interconnected systems with
applications to biochemical networks: an input-output approach},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1367-1379},
VOLUME = {55},
PDF = {../../FTPDIR/scardovi_arcak_sontag_TAC2010.pdf},
ABSTRACT = {This paper provides synchronization conditions for
networks of nonlinear systems, where each component of the network
itself consists of subsystems represented as operators in the
extended L2 space. The synchronization conditions are provided by
combining the input-output properties of the subsystems with
information about the structure of network. The paper also explores
results for state-space models as well as biochemical applications.
The work is motivated by cellular networks where signaling occurs
both internally, through interactions of species, and externally,
through intercellular signaling. }
}
@ARTICLE{shoval10,
AUTHOR = {O. Shoval and L. Goentoro and Y. Hart and A. Mayo and
E.D. Sontag and U. Alon},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Fold change detection and scalar symmetry of sensory
input fields},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {15995-16000},
VOLUME = {107},
KEYWORDS = {identifiability, adaptation, biological adaptation,
perfect adaptation, adaptation, feedforward loops, integral feedback,
scale invariance, systems biology, transient behavior, symmetries,
fcd, fold-change detection, incoherent feedforward loop, feedforward,
IFFL},
PDF = {../../FTPDIR/shoval-et_al_pnas2010_online.pdf},
ABSTRACT = {Certain cellular sensory systems display fold-change
detection (FCD): a response whose entire shape, including amplitude
and duration, depends only on fold-changes in input, and not on
absolute changes. Thus, a step change in input from, say, level 1 to
2, gives precisely the same dynamical output as a step from level 2
to 4, since the steps have the same fold-change. We ask what is the
benefit of FCD, and show that FCD is necessary and sufficient for
sensory search to be independent of multiplying the input-field by a
scalar. Thus the FCD search pattern depends only on the spatial
profile of the input, and not on its amplitude. Such scalar symmetry
occurs in a wide range of sensory inputs, such as source strength
multiplying diffusing/convecting chemical fields sensed in
chemotaxis, ambient light multiplying the contrast field in vision,
and protein concentrations multiplying the output in cellular
signaling-systems.Furthermore, we demonstrate that FCD entails two
features found across sensory systems, exact adaptation and Weber's
law, but that these two features are not sufficient for FCD. Finally,
we present a wide class of mechanisms that have FCD, including
certain non-linear feedback and feedforward loops.. We find that
bacterial chemotaxis displays feedback within the present class, and
hence is expected to show FCD. This can explain experiments in which
chemotaxis searches are insensitive to attractant source levels. This
study thus suggests a connection between properties of biological
sensory systems and scalar symmetry stemming from physical properties
of their input-fields.}
}
@ARTICLE{feedforward_circuits_adaptation,
AUTHOR = {E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {Remarks on Feedforward Circuits, Adaptation, and Pulse
Memory},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {39-51},
VOLUME = {4},
KEYWORDS = {adaptation, feedforward loops, integral feedback,
systems biology, transient behavior, incoherent feedforward loop,
feedforward, IFFL},
PDF = {../../FTPDIR/feedforward_adapt_iet_sysbio2010.pdf},
ABSTRACT = { This note studies feedforward circuits as models for
perfect adaptation to step signals in biological systems. A global
convergence theorem is proved in a general framework, which includes
examples from the literature as particular cases. A notable aspect of
these circuits is that they do not adapt to pulse signals, because
they display a memory phenomenon. Estimates are given of the
magnitude of this effect. }
}
@ARTICLE{kalman2010,
AUTHOR = {E.D. Sontag},
JOURNAL = {Control Systems Magazine},
TITLE = {Rudolf E. Kalman and his students},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {87-103},
VOLUME = {30},
PDF = {../../FTPDIR/kalman_students_article_2010.pdf},
ABSTRACT = {An edited set of articles about Rudolf Kalman's legacy
through his Ph.D. students.}
}
@ARTICLE{mvp,
AUTHOR = {E.D. Sontag and D. Zeilberger},
JOURNAL = {Advances in Applied Mathematics},
TITLE = {A symbolic computation approach to a problem involving
multivariate Poisson distributions},
YEAR = {2010},
OPTMONTH = {},
NOTE = {There are typos in the published version. Please see this file for corrections: https://drive.google.com/file/d/0BzWFHczJF2INUlEtVkFJOUJiUFU/view},
OPTNUMBER = {},
PAGES = {359-377},
VOLUME = {44},
KEYWORDS = {probability theory, stochastic systems, systems biology,
reaction networks, chemical master equation},
PDF = {../../FTPDIR/sontag_zeilberger_aam2010.pdf},
ABSTRACT = {Multivariate Poisson random variables subject to linear
integer constraints arise in several application areas, such as
queuing and biomolecular networks. This note shows how to compute
conditional statistics in this context, by employing WZ Theory and
associated algorithms. A symbolic computation package has been
developed and is made freely available. A discussion of motivating
biomolecular problems is also provided. }
}
@ARTICLE{liming_patrick_jmb10,
AUTHOR = {L. Wang and de Leenheer, P. and E.D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Conditions for global stability of monotone tridiagonal
systems with negative feedback},
YEAR = {2010},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {138-130},
VOLUME = {59},
KEYWORDS = {systems biology, monotone systems, tridiagonal systems,
global stability},
PDF = {../../FTPDIR/wang_leenheer_sontag_scl2010.pdf},
ABSTRACT = {This paper studies monotone tridiagonal systems with
negative feedback. These systems possess the Poincar{\'e}-Bendixson
property, which implies that, if orbits are bounded, if there is a
unique steady state and this unique equilibrium is asymptotically
stable, and if one can rule out periodic orbits, then the steady
state is globally asymptotically stable. Different approaches are
discussed to rule out period orbits. One is based on direct
linearization, while the other uses the theory of second additive
compound matrices. Among the examples that will illustrate our main
theoretical results is the classical Goldbeter model of circadian
rhythms. }
}
@INPROCEEDINGS{10cdc_russo,
AUTHOR = {G. Russo and di Bernardo, M. and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010},
TITLE = {Stability of networked systems: a multi-scale approach
using contraction},
YEAR = {2010},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {FrB14.3},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {contractive systems, contractions, systems biology,
reaction networks, synchronization},
ABSTRACT = {Preliminary conference version of ''A contraction
approach to the hierarchical analysis and design of networked
systems''.}
}
@INPROCEEDINGS{10cdc_mra,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Atlanta, Dec. 2010},
TITLE = {Remarks on structural identification, modularity, and
retroactivity},
YEAR = {2010},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {ThA23.1},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {modularity, retroactivity, identification},
PDF = {../../FTPDIR/modularity_retroactivity_sontag_cdc2010.pdf},
ABSTRACT = {Summarized conference version of ``Modularity,
retroactivity, and structural identification''.}
}
@INPROCEEDINGS{white_CVPR2010poster,
AUTHOR = {A. White and P.G. Cipriani and H.-L. Kao and B. Lees and
D. Geiger and E.D. Sontag and K. Gunsalus and F. Piano},
BOOKTITLE = {2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
TITLE = {Rapid and accurate developmental stage recognition of C.
elegans from high-throughput image data},
YEAR = {2010},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3089-3096},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/white_celegans_cvpr2010.pdf},
ABSTRACT = {This paper presents a hierarchical principle for object
recognition and its application to automatically classify
developmental stages of C. elegans animals from a population of mixed
stages. The system is in current use in a functioning C. elegans
laboratory and has processed over two hundred thousand images for lab
users.}
}
@INCOLLECTION{angeli_sontag_mitbook09,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Control Theory in Systems Biology},
PUBLISHER = {MIT Press},
TITLE = {Graphs and the Dynamics of Biochemical Networks},
YEAR = {2009},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {B.P. Ingalls and P. Iglesias},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {125-142},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
ABSTRACT = { This is an expository paper about graph-theoretical
properties of biochemical networks, discussing two approaches, one
based on bipartite graphs and Petri net concepts, and another based
on decompositions into order-preserving subsystems. Other papers on
this website contain basically the same material. }
}
@INCOLLECTION{delvecchio_sontag_mitbook09,
AUTHOR = {Del Vecchio, D. and E.D. Sontag},
BOOKTITLE = {Control Theory in Systems Biology},
PUBLISHER = {MIT Press},
TITLE = {Synthetic Biology: A Systems Engineering Perspective},
YEAR = {2009},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {B.P. Ingalls and P. Iglesias},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {101-123},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
ABSTRACT = { This is an expository paper about certain aspects of
Synthetic Biology, including a discussion of the issue of modularity
(load effects from downstream components). }
}
@ARTICLE{angeli_hirsch_sontag_jde09,
AUTHOR = {D. Angeli and M.W. Hirsch and E.D. Sontag},
JOURNAL = {J. of Differential Equations},
TITLE = {Attractors in coherent systems of differential equations},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {3058-3076},
VOLUME = {246},
KEYWORDS = {monotone systems, positive feedback systems},
PDF = {../../FTPDIR/hirsch_angeli_sontag_jde09_ps2pdf.pdf},
ABSTRACT = {Attractors of cooperative dynamical systems are
particularly simple; for example, a nontrivial periodic orbit cannot
be an attractor. This paper provides characterizations of attractors
for the wider class of systems defined by the property that all
directed feedback loops are positive. Several new results for
cooperative systems are obtained in the process.}
}
@ARTICLE{biotechprogress08,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
JOURNAL = {Biotechnology Progress},
TITLE = {Chemical networks with inflows and outflows: A positive
linear differential inclusions approach},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {632-642},
VOLUME = {25},
KEYWORDS = {reaction networks, fluxes, differential inclusions,
positive systems, Petri nets, persistence, switched systems},
PDF = {../../FTPDIR/angeli_leenheer_sontag_biotech08.pdf},
ABSTRACT = {Certain mass-action kinetics models of biochemical
reaction networks, although described by nonlinear differential
equations, may be partially viewed as state-dependent linear
time-varying systems, which in turn may be modeled by convex compact
valued positive linear differential inclusions. A result is provided
on asymptotic stability of such inclusions, and applied to
biochemical reaction networks with inflows and outflows. Included is
also a characterization of exponential stability of general
homogeneous switched systems }
}
@ARTICLE{chaves_sengupta07,
AUTHOR = {M. Chaves and A. M. Sengupta and E.D. Sontag},
JOURNAL = {J. of Mathematical Biology},
TITLE = {Geometry and topology of parameter space: investigating
measures of robustness in regulatory networks},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {315-358},
VOLUME = {59},
KEYWORDS = {identifiability, robust, robustness, geometry},
PDF = {../../FTPDIR/chaves_sengupta_sontag_j_math_biology_2009.pdf},
ABSTRACT = {The concept of robustness of regulatory networks has
been closely related to the nature of the interactions among genes,
and the capability of pattern maintenance or reproducibility.
Defining this robustness property is a challenging task, but
mathematical models have often associated it to the volume of the
space of admissible parameters. Not only the volume of the space but
also its topology and geometry contain information on essential
aspects of the network, including feasible pathways, switching
between two parallel pathways or distinct/disconnected active regions
of parameters. A method is presented here to characterize the space
of admissible parameters, by writing it as a semi-algebraic set, and
then theoretically analyzing its topology and geometry, as well as
volume. This method provides a more objective and complete measure of
the robustness of a developmental module. As a detailed case study,
the segment polarity gene network is analyzed. }
}
@ARTICLE{adel,
AUTHOR = {A. Dayarian and M. Chaves and E.D. Sontag and
A. M. Sengupta},
JOURNAL = {PLoS Computational Biology},
TITLE = {Shape, Size and Robustness: Feasible Regions in the
Parameter Space of Biochemical Networks},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e10000256},
VOLUME = {5},
KEYWORDS = {identifiability, robust, robustness, geometry},
PDF = {../../FTPDIR/dayarian_chaves_sontag_sengupta_plos09.pdf},
ABSTRACT = {The concept of robustness of regulatory networks has
received much attention in the last decade. One measure of robustness
has been associated with the volume of the feasible region, namely,
the region in the parameter space in which the system is functional.
In recent work, we emphasized that topology and geometry matter, as
well as volume. In this paper, and using the segment polarity gene
network to illustrate our approach, we show that random walks in
parameter space and how they exit the feasible region provide a rich
perspective on the different modes of failure of a model. In
particular, for the segment polarity network, we found that, between
two alternative ways of activating Wingless, one is more robust. Our
method provides a more complete measure of robustness to parameter
variation. As a general modeling strategy, our approach is an
interesting alternative to Boolean representation of biochemical
networks. }
}
@ARTICLE{ddv_ecc09,
AUTHOR = {Del Vecchio, D. and E.D. Sontag},
JOURNAL = {European Journal of Control},
TITLE = {Engineering Principles in Bio-Molecular Systems: From
Retroactivity to Modularity},
YEAR = {2009},
OPTMONTH = {},
NOTE = {Preliminary version appeared as paper MoB2.2 in Proceedings of the European Control Conference 2009, August 23-26, 2009, Budapest},
OPTNUMBER = {},
PAGES = {389-397},
VOLUME = {15},
KEYWORDS = {systems biology, reaction networks, synthetic biology,
futile cycles, singular perturbations, modularity},
PDF = {../../FTPDIR/delvecchio_sontag_european_j_control2009_engineering_principles_in_biomolecular_systems.pdf}
}
@ARTICLE{riley07hmm,
AUTHOR = {T. Riley and X. Yu and E.D. Sontag and A. Levine},
JOURNAL = {BMC Bioinformatics},
TITLE = {The P53HMM algorithm: using novel profile Hidden Markov
Models to detect p53-responsive genes},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {111},
VOLUME = {10},
KEYWORDS = {Hidden Markov Models, p53, transcription factors},
PDF = {../../FTPDIR/riley_yu_sontag_levine_p53hmm_bmc_bioinformatics09.pdf},
ABSTRACT = { A novel computational method (called p53HMM) is
presented that utilizes Profile Hidden Markov Models (PHMM's) to
estimate the relative binding affinities of putative p53 response
elements (RE's), both p53 single-sites and cluster-sites. These
models incorporate a novel ``Correlated Baum Welch'' training
algorithm that provides increased predictive power by exploiting the
redundancy of information found in the repeated, palindromic
p53-binding motif. The predictive accuracy of these new models are
compared against other predictive models, including position specic
score matrices (PSSM's, or weight matrices). Finally, we provide
experimental evidence that verifies a predicted p53-target site that
regu- lates the CHMP4C gene. The P53HMM algorithm is available
on-line from http://tools.csb.ias.edu. },
DOI = {10.1186/1471-2105-10-111}
}
@ARTICLE{sontag-wang-megretski-tac,
AUTHOR = {E.D. Sontag and Y. Wang and A. Megretski},
JOURNAL = {IEEE Transactions Autom. Control},
TITLE = {Input classes for identification of bilinear systems},
YEAR = {2009},
OPTMONTH = {},
NOTE = {Also arXiv math.OC/0610633, 20 Oct 2006, and short version in ACC'07.},
OPTNUMBER = {},
PAGES = {195-207},
VOLUME = {54},
KEYWORDS = {realization theory, observability, identifiability,
bilinear systems},
PDF = {../../FTPDIR/sontag_wang_megretski_inputs_tac_54_195_207.pdf},
ABSTRACT = { This paper asks what classes of input signals are
sufficient in order to completely identify the input/output behavior
of generic bilinear systems. The main results are that step inputs
are not sufficient, nor are single pulses, but the family of all
pulses (of a fixed amplitude but varying widths) do suffice for
identification. }
}
@ARTICLE{weinstein07,
AUTHOR = {A.M. Weinstein and E.D. Sontag},
JOURNAL = {Bulletin of Mathematical Biology},
TITLE = {Modeling proximal tubule cell homeostasis: Tracking
changes in luminal flow},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1285-1322},
VOLUME = {71},
PDF = {../../FTPDIR/weinstein_sontag_bulletin_math_biology_proximal_tubule_2009.pdf},
ABSTRACT = {During normal kidney function, there are are routinely
wide swings in proximal tubule fluid flow and proportional changes in
Na+ reabsorption across tubule epithelial cells. This
"glomerulotubular balance" occurs in the absence of any substantial
change in cell volume, and is thus a challenge to coordinate luminal
membrane solute entry with peritubular membrane solute exit. In this
work, linear optimal control theory is applied to generate a
configuration of regulated transporters that could achieve this
result. A previously developed model of rat proximal tubule
epithelium is linearized about a physiologic reference condition; the
approximate linear system is recast as a dynamical system; and a
Riccati equation is solved to yield optimal linear feedback that
stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback
control is largely consigned to three physiologic variables, cell
volume, cell electrical potential, and lateral intercellular
hydrostatic pressure. Transport modulation by cell volume stabilizes
cell volume; transport modulation by electrical potential or
interspace pressure act to stabilize Na+ flux and cell pH. This
feedback control is utilized in a tracking problem, in which
reabsorptive Na+ flux varies over a factor of two. The resulting
control parameters consist of two terms, an autonomous term and a
feedback term, and both terms include transporters on both luminal
and peritubular cell membranes. Overall, the increase in Na+ flux is
achieved with upregulation of luminal Na+/H+ exchange and Na+-glucose
cotransport, with increased peritubular Na+-3HCO_3- and K+-Cl-
cotransport, and with increased Na+,K+-ATPase activity. The
configuration of activated transporters emerges as testable
hypothesis of the molecular basis for glomerulotubular balance. It is
suggested that the autonomous control component at each cell membrane
could represent the cytoskeletal effects of luminal flow. }
}
@INPROCEEDINGS{09cdc_angeli_leenheer,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009},
TITLE = {On persistence of chemical reaction networks with
time-dependent kinetics and no global conservation laws},
YEAR = {2009},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4559-4564},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {reaction networks, fluxes, Petri nets, persistence,
reaction networks with inputs},
PDF = {../../FTPDIR/09cdc_persistence_from_ieee.pdf},
ABSTRACT = {This is a very summarized version ofthe first part of
the paper "Persistence results for chemical reaction networks with
time-dependent kinetics and no global conservation laws". }
}
@INPROCEEDINGS{09cdc_scardovi_arcak_part1,
AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009},
TITLE = {Synchronization of interconnected systems with an
input-output approach. Part I: Main results},
YEAR = {2009},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {First part of conference version of journal paper.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {609-614},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {passive systems, secant condition, reaction networks,
systems biology},
ABSTRACT = {See abstract and link to pdf in entry for Journal paper. }
}
@INPROCEEDINGS{09cdc_scardovi_arcak_part2,
AUTHOR = {L. Scardovi and M. Arcak and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Shanhai, Dec. 2009},
TITLE = {Synchronization of interconnected systems with an
input-output approach. Part II: State-Space result and application to
biochemical networks},
YEAR = {2009},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Second part of conference version of journal paper.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {615-620},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {passive systems, secant condition, reaction networks,
systems biology},
ABSTRACT = {See abstract and link to pdf in entry for Journal paper. }
}
@TECHREPORT{arxiv_chaos_2009,
AUTHOR = {E.D. Sontag},
INSTITUTION = {arxiv 0906.2166},
TITLE = {An observation regarding systems which converge to
steady states for all constant inputs, yet become chaotic with
periodic inputs},
YEAR = {2009},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTTYPE = {},
PDF = {http://arxiv.org/pdf/0906.2166}
}
@INCOLLECTION{SontagArcakSagarBook08,
AUTHOR = {M. Arcak and E.D. Sontag},
BOOKTITLE = {Recent Advances in Learning and Control},
PUBLISHER = {Springer-Verlag, NY},
TITLE = {Passivity-based Stability of Interconnection Structures},
YEAR = {2008},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {V. Blondel and S. Boyd and H. Kimura},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {195-204},
OPTSERIES = {},
OPTTYPE = {},
VOLUME = {Volume 371},
KEYWORDS = {passive systems, secant condition, reaction networks},
PDF = {../../FTPDIR/sontag_arcak_vidyasagar_book.pdf},
ABSTRACT = {In this expository paper, we provide a streamlined
version of the key lemma on stability of interconnections due to
Vidyasagar and Moylan and Hill, and then show how it its hypotheses
may be verified for network structures of great interest in biology.},
DOI = {10.1007/978-1-84800-155-8_14}
}
@ARTICLE{dasgupta-albert,
AUTHOR = {R. Albert and B. Dasgupta and R. Dondi and E.D. Sontag},
JOURNAL = {Algorithmica},
TITLE = {Inferring (biological) signal transduction networks via
transitive reductions of directed graphs},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {129-159},
VOLUME = {51},
KEYWORDS = {systems biology, reaction networks, algorithms,
signal transduction networks, graph algorithms},
PDF = {../../FTPDIR/albert_dasgupta_dondi_sontag_algorithmica.pdf},
ABSTRACT = {The transitive reduction problem is that of inferring a
sparsest possible biological signal transduction network consistent
with a set of experimental observations, with a goal to minimize
false positive inferences even if risking false negatives. This paper
provides computational complexity results as well as approximation
algorithms with guaranteed performance.},
DOI = {10.1007/s00453-007-9055-0}
}
@ARTICLE{IEEEsysbio_AS,
AUTHOR = {D. Angeli and E.D. Sontag},
JOURNAL = {IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology},
TITLE = {Oscillations in I/O monotone systems},
YEAR = {2008},
OPTMONTH = {},
NOTE = {Preprint version in arXiv q-bio.QM/0701018, 14 Jan 2007},
OPTNUMBER = {},
PAGES = {166-176},
VOLUME = {55},
KEYWORDS = {monotone systems, hopf bifurcations, circadian rhythms,
tridiagonal systems, nonlinear dynamics, systems biology,
reaction networks, oscillations, periodic behavior,
delay-differential systems},
PDF = {../../FTPDIR/angeli_sontag_circadian_TAC_CAS_2008.pdf},
ABSTRACT = {In this note, we show how certain properties of
Goldbeter's 1995 model for circadian oscillations can be proved
mathematically, using techniques from the recently developed theory
of monotone systems with inputs and outputs. The theory establishes
global asymptotic stability, and in particular no oscillations, if
the rate of transcription is somewhat smaller than that assumed by
Goldbeter, based on the application of a tight small gain condition.
This stability persists even under arbitrary delays in the feedback
loop. On the other hand, when the condition is violated a
Poincare'-Bendixson result allows to conclude existence of
oscillations, for sufficiently high delays.}
}
@ARTICLE{translation-invariance,
AUTHOR = {D. Angeli and E.D. Sontag},
JOURNAL = {Nonlinear Analysis Series B: Real World Applications},
TITLE = {Translation-invariant monotone systems, and a global
convergence result for enzymatic futile cycles},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {128-140},
VOLUME = {9},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli_sontag_translationinvariance_nonlinear_analysis08.pdf},
ABSTRACT = { Strongly monotone systems of ordinary differential
equations which have a certain translation-invariance property are
shown to have the property that all projected solutions converge to a
unique equilibrium. This result may be seen as a dual of a well-known
theorem of Mierczynski for systems that satisfy a conservation law.
As an application, it is shown that enzymatic futile cycles have a
global convergence property. },
DOI = {10.1016/j.nonrwa.2006.09.006}
}
@ARTICLE{arcak-sontag-MBSE07,
AUTHOR = {M. Arcak and E.D. Sontag},
JOURNAL = {Mathematical Biosciences and Engineering},
TITLE = {A passivity-based stability criterion for a class of
interconnected systems and applications to biochemical reaction
networks},
YEAR = {2008},
OPTMONTH = {},
NOTE = {Also, preprint: arxiv0705.3188v1 [q-bio], May 2007},
OPTNUMBER = {},
PAGES = {1-19},
VOLUME = {5},
KEYWORDS = {MAPK cascades, systems biology, reaction networks,
cyclic feedback systems, secant condition, nonlinear stability,
dynamical systems},
PDF = {../../FTPDIR/arcak_sontag_MBE_2008_galleys.pdf},
ABSTRACT = {This paper presents a stability test for a class of
interconnected nonlinear systems motivated by biochemical reaction
networks. One of the main results determines global asymptotic
stability of the network from the diagonal stability of a
"dissipativity matrix" which incorporates information about the
passivity properties of the subsystems, the interconnection structure
of the network, and the signs of the interconnection terms. This
stability test encompasses the "secant criterion" for cyclic networks
presented in our previous paper, and extends it to a general
interconnection structure represented by a graph. A second main
result allows one to accommodate state products. This extension makes
the new stability criterion applicable to a broader class of models,
even in the case of cyclic systems. The new stability test is
illustrated on a mitogen activated protein kinase (MAPK) cascade
model, and on a branched interconnection structure motivated by
metabolic networks. Finally, another result addresses the robustness
of stability in the presence of diffusion terms in a compartmental
system made out of identical systems.}
}
@ARTICLE{ddv07,
AUTHOR = {Del Vecchio, D. and A.J. Ninfa and E.D. Sontag},
JOURNAL = {Molecular Systems Biology},
TITLE = {Modular Cell Biology: Retroactivity and Insulation},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {161},
VOLUME = {4},
KEYWORDS = {retroactivity, systems biology, reaction networks,
synthetic biology, futile cycles, singular perturbations, modularity},
PDF = {../../FTPDIR/delvecchio-ninfa-sontag-MSB2008-paper-and-supplement.pdf},
ABSTRACT = {Modularity plays a fundamental role in the prediction of
the behavior of a system from the behavior of its components,
guaranteeing that the properties of individual components do not
change upon interconnection. Just as electrical, hydraulic, and other
physical systems often do not display modularity, nor do many
biochemical systems, and specifically, genetic networks. Here, we
study the effect of interconnections on the input/output dynamic
characteristics of transcriptional components, focusing on a
property, which we call "retroactivity," that plays a role analogous
to non-zero output impedance in electrical systems. In
transcriptional networks, retroactivity is large when the amount of
transcription factor is comparable to, or smaller than, the amount of
promoter binding sites, or when the affinity of such binding sites is
high. In order to attenuate the effect of retroactivity, we propose a
feedback mechanism inspired by the design of amplifiers in
electronics. We introduce, in particular, a mechanism based on a
phosphorylation/dephosphorylation cycle. This mechanism enjoys a
remarkable insulation property, due to the fast time scales of the
phosphorylation and dephosphorylation reactions. Such a mechanism,
when viewed as a signal transduction system, has thus an inherent
capacity to provide insulation and hence to increase the modularity
of the system in which it is placed.}
}
@ARTICLE{enciso_multi_submitted,
AUTHOR = {G.A. Enciso and E.D. Sontag},
JOURNAL = {Journal of Biological Dynamics},
TITLE = {Monotone bifurcation graphs},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {121-139},
VOLUME = {2},
PDF = {../../FTPDIR/enciso_sontag_multicharacteristics_journal_biological_dynamics_2008.pdf},
ABSTRACT = {This paper generalizes the approach to bistability based
on the existence of characteristics for open-loop monotone systems to
the case when characteristics do not exist. A set-valued version is
provided, instead.}
}
@ARTICLE{IEEEsysbio_JAS,
AUTHOR = {M.R. Jovanovic and M. Arcak and E.D. Sontag},
JOURNAL = {IEEE Transactions on Circuits and Systems, Special Issue on Systems Biology},
TITLE = {A passivity-based approach to stability of spatially
distributed systems with a cyclic interconnection structure},
YEAR = {2008},
OPTMONTH = {},
NOTE = {Preprint: also arXiv math.OC/0701622, 22 January 2007.},
OPTNUMBER = {},
PAGES = {75-86},
VOLUME = {55},
KEYWORDS = {MAPK cascades, systems biology, reaction networks,
nonlinear stability, nonlinear dynamics, diffusion, secant condition,
cyclic feedback systems},
PDF = {../../FTPDIR/jovanovic_arcak_sontag_TAC_CAS2008.pdf},
ABSTRACT = {A class of distributed systems with a cyclic
interconnection structure is considered. These systems arise in
several biochemical applications and they can undergo diffusion
driven instability which leads to a formation of spatially
heterogeneous patterns. In this paper, a class of cyclic systems in
which addition of diffusion does not have a destabilizing effect is
identified. For these systems global stability results hold if the
"secant" criterion is satisfied. In the linear case, it is shown that
the secant condition is necessary and sufficient for the existence of
a decoupled quadratic Lyapunov function, which extends a recent
diagonal stability result to partial differential equations. For
reaction-diffusion equations with nondecreasing coupling
nonlinearities global asymptotic stability of the origin is
established. All of the derived results remain true for both linear
and nonlinear positive diffusion terms. Similar results are shown for
compartmental systems.}
}
@ARTICLE{dasgupta-albert3,
AUTHOR = {S. Kachalo and R. Zhang and E.D. Sontag and R. Albert and
B. Dasgupta},
JOURNAL = {Bioinformatics},
TITLE = {NET-SYNTHESIS: A software for synthesis, inference and
simplification of signal transduction networks},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {293 - 295},
VOLUME = {24},
KEYWORDS = {systems biology, reaction networks, algorithms,
signal transduction networks, graph algorithms},
PDF = {../../FTPDIR/kachalo_zhang_sontag_albert_dasgupta_bioinformatics08.pdf},
ABSTRACT = {This paper presents a software tool for inference and
simplification of signal transduction networks. The method relies on
the representation of observed indirect causal relationships as
network paths, using techniques from combinatorial optimization to
find the sparsest graph consistent with all experimental
observations. We illustrate the biological usability of our software
by applying it to a previously published signal transduction network
and by using it to synthesize and simplify a novel network
corresponding to activation-induced cell death in large granular
lymphocyte leukemia.}
}
@ARTICLE{maayan07,
AUTHOR = {A. Maayan and R. Iyengar and E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {Intracellular Regulatory Networks are close to Monotone
Systems},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {103-112},
VOLUME = {2},
PDF = {../../FTPDIR/maayan_lipshtat_iyengar_sontag_IETsystemsbio08.pdf},
ABSTRACT = {We find that three intracellular regulatory networks
contain far more positive "sign-consistent" feedback and feed-forward
loops than negative loops. Negative inconsistent loops can be more
easily removed from real regulatory network topologies compared to
removing negative loops from shuffled networks. The abundance of
positive feed-forward loops and feedback loops in real networks
emerges from the presence of hubs that are enriched with either
negative or positive links, and from the non-uniform connectivity
distribution. Boolean dynamics applied to the signaling network
further support the stability of its topology. These observations
suggest that the "close-to-monotone" structure of intracellular
regulatory networks may contribute to the dynamical stability
observed in cellular behavior.}
}
@ARTICLE{riley07,
AUTHOR = {T. Riley and E.D. Sontag and P. Chen and A. Levine},
JOURNAL = {Nature Reviews Molecular Cell Biology},
TITLE = {The transcriptional regulation of human p53-regulated
genes},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {402-412},
VOLUME = {9},
KEYWORDS = {Hidden Markov Models, p53, transcription},
PDF = {../../FTPDIR/riley_sontag_chen_levine_p53_nature_reviews_cell_bio_2008_including_supplements.pdf},
ABSTRACT = { The p53 protein regulates the transcription of many
different genes in response to a wide variety of stress signals.
Following DNA damage, p53 regulates key processes, including DNA
repair, cell-cycle arrest, senescence and apoptosis, in order to
suppress cancer. This Analysis article provides an overview of the
current knowledge of p53-regulated genes in these pathways and
others, and the mechanisms of their regulation. In addition, we
present the most comprehensive list so far of human p53-regulated
genes and their experimentally validated, functional binding sites
that confer p53 regulation. }
}
@ARTICLE{essays_biochemistry,
AUTHOR = {E.D. Sontag},
JOURNAL = {Essays in Biochemistry},
TITLE = {Network reconstruction based on steady-state data},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {161-176},
VOLUME = {45},
KEYWORDS = {modular response analysis, systems biology,
reaction networks, reverse engineering, gene and protein networks,
protein networks, gene networks, systems identification,
MAPK cascades},
PUBLISHER = {Portland Press},
PDF = {../../FTPDIR/unravel_essays_biochem_reprint.pdf},
ABSTRACT = { The ``reverse engineering problem'' in systems biology
is that of unraveling of the web of interactions among the components
of protein and gene regulatory networks, so as to map out the direct
or local interactions among components. These direct interactions
capture the topology of the functional network. An intrinsic
difficulty in capturing these direct interactions, at least in intact
cells, is that any perturbation to a particular gene or signaling
component may rapidly propagate throughout the network, thus causing
global changes which cannot be easily distinguished from direct
effects. Thus, a major goal in reverse engineering is to use these
observed global responses - such as steady-state changes in
concentrations of active proteins, mRNA levels, or transcription
rates - in order to infer the local interactions between individual
nodes. One approach to solving this global-to-local problem is the
``Modular Response Analysis'' (MRA) method proposed in work of the
author with Kholodenko et. al. (PNAS, 2002) and further elaborated in
other papers. The basic method deals only with steady-state data.
However, recently, quasi-steady state MRA has been used by Santos et.
al. (Nature Cell Biology, 2007) for quantifying positive and negative
feedback effects in the Raf/Mek/Erk MAPK network in rat adrenal
pheochromocytoma (PC-12) cells. This paper presents an overview of
the MRA technique, as well as a generalization of the algorithm to
that quasi-steady state case. }
}
@ARTICLE{sontag_laubenbacher_jarrah07,
AUTHOR = {E.D. Sontag and A. Veliz-Cuba and R. Laubenbacher and
A.S. Jarrah},
JOURNAL = {Biophysical Journal},
TITLE = {The effect of negative feedback loops on the dynamics of
Boolean networks},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {518-526},
VOLUME = {95},
KEYWORDS = {monotone systems, positive feedback systems,
Boolean networks, limit cycles},
PDF = {../../FTPDIR/sontag_cuba_laubenbacher_jarrah_biophysical_journal_2008.pdf},
ABSTRACT = {Feedback loops play an important role in determining the
dynamics of biological networks. In order to study the role of
negative feedback loops, this paper introduces the notion of
"distance to positive feedback (PF-distance)" which in essence
captures the number of "independent" negative feedback loops in the
network, a property inherent in the network topology. Through a
computational study using Boolean networks it is shown that
PF-distance has a strong influence on network dynamics and correlates
very well with the number and length of limit cycles in the phase
space of the network. To be precise, it is shown that, as the number
of independent negative feedback loops increases, the number (length)
of limit cycles tends to decrease (increase). These conclusions are
consistent with the fact that certain natural biological networks
exhibit generally regular behavior and have fewer negative feedback
loops than randomized networks with the same numbers of nodes and
connectivity. }
}
@ARTICLE{arxiv:futileequilibria,
AUTHOR = {L. Wang and E.D. Sontag},
JOURNAL = {Journal of Mathematical Biology},
TITLE = {On the number of steady states in a multiple futile
cycle},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {29-52},
VOLUME = {57},
KEYWORDS = {singular perturbations, futile cycles, MAPK cascades,
systems biology, reaction networks, multistability},
PDF = {../../FTPDIR/liming_wang_sontag_futile_cycles_JMB08.pdf},
ABSTRACT = {This note studies the number of positive steady states
in biomolecular reactions consisting of activation/deactivation
futile cycles, such as those arising from phosphorylations and
dephosphorylations at each level of a MAPK cascade. It is shown that:
(1) for some parameter ranges, there are at least n+1 (if n is even)
or n (if n is odd) steady states; (2) there never are more than 2n-1
steady states (so, for n=2, there are no more than 3 steady states);
(3) for parameters near the standard Michaelis-Menten quasi-steady
state conditions, there are at most n+1 steady states; and (4) for
parameters far from the standard Michaelis-Menten quasi-steady state
conditions, there is at most one steady state.}
}
@ARTICLE{wang:JNS07,
AUTHOR = {L. Wang and E.D. Sontag},
JOURNAL = {J. Nonlinear Science},
TITLE = {Singularly perturbed monotone systems and an application
to double phosphorylation cycles},
YEAR = {2008},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {527-550},
VOLUME = {18},
KEYWORDS = {singular perturbations, futile cycles, MAPK cascades,
systems biology, reaction networks, nonlinear stability,
nonlinear dynamics, multistability, monotone systems},
PDF = {../../FTPDIR/wang_sontag_JNS08.pdf},
ABSTRACT = {The theory of monotone dynamical systems has been found
very useful in the modeling of some gene, protein, and signaling
networks. In monotone systems, every net feedback loop is positive.
On the other hand, negative feedback loops are important features of
many systems, since they are required for adaptation and precision.
This paper shows that, provided that these negative loops act at a
comparatively fast time scale, the main dynamical property of
(strongly) monotone systems, convergence to steady states, is still
valid. An application is worked out to a double-phosphorylation
"futile cycle" motif which plays a central role in eukaryotic cell
signaling The workis heavily based on Fenichel-Jones geometric
singular perturbation theory.}
}
@INPROCEEDINGS{iglesias_ifac08,
AUTHOR = {B. Andrews and E.D. Sontag and P. Iglesias},
BOOKTITLE = {Proc. 17th IFAC World Congress, Seoul},
TITLE = {An approximate internal model principle: Applications to
nonlinear models of biological systems},
YEAR = {2008},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {Paper FrB25.3, 6 pages},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {biological adaptation, internal model principle},
PDF = {../../FTPDIR/andrews_sontag_iglesias_approximate_internal_model_IFAC2008.pdf},
ABSTRACT = {The proper function of many biological systems requires
that external perturbations be detected, allowing the system to adapt
to these environmental changes. It is now well established that this
dual detection and adaptation requires that the system have an
internal model in the feedback loop. In this paper we relax the
requirement that the response of the system adapt perfectly, but
instead allow regulation to within a neighborhood of zero. We show,
in a nonlinear setting, that systems with the ability to detect input
signals and approximately adapt require an approximate model of the
input. We illustrate our results by analyzing a well-studied
biological system. These results generalize previous work which
treats the perfectly adapting case. }
}
@INPROCEEDINGS{ddv_acc08,
AUTHOR = {Del Vecchio, D. and A.J. Ninfa and E.D. Sontag},
BOOKTITLE = {Proceedings of the 2008 American Control Conference, Seattle, June 2008},
TITLE = {A Systems Theory with Retroactivity: Application to
Transcriptional Modules},
YEAR = {2008},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {Paper WeC04.1},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {retroactivity, systems biology, reaction networks,
synthetic biology, futile cycles, singular perturbations, modularity},
PDF = {../../FTPDIR/delvecchio_ninfa_sontag_retroactivity_acc2008.pdf}
}
@INPROCEEDINGS{08cdc_liming,
AUTHOR = {L. Wang and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Cancun, Dec. 2008},
TITLE = {Global stability for monotone tridiagonal systems with
negative feedback},
YEAR = {2008},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4091-4096},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, monotone systems, tridiagonal systems,
global stability},
ABSTRACT = {Conference version of paper "Conditions for global
stability of monotone tridiagonal systems with negative feedback"}
}
@INCOLLECTION{dasgupta-albert2b,
AUTHOR = {R. Albert and B. DasGupta and R. Dondi and S. Kachalo and
E.D. Sontag and A. Zelikovsky and K. Westbrooks},
BOOKTITLE = {7th Workshop on Algorithms in Bioinformatics (WABI)},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {A novel method for signal transduction network inference
from indirect experimental evidence},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {R. Giancarlo and S. Hannenhalli},
OPTMONTH = {},
NOTE = {Conference version of journal paper with same title},
OPTNUMBER = {},
PAGES = {407-419},
OPTSERIES = {},
OPTTYPE = {},
VOLUME = {14},
KEYWORDS = {systems biology, reaction networks, algorithms,
signal transduction networks, graph algorithms}
}
@INCOLLECTION{angeli_leenheer_petri_toulouse,
AUTHOR = {D. Angeli and De Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357)},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {A Petri net approach to persistence analysis in chemical
reaction networks},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {I. Queinnec and S. Tarbouriech and G. Garcia and
S-I. Niculescu},
OPTMONTH = {},
NOTE = {See abstract for A Petri net approach to the study of persistence in chemical reaction networks.},
OPTNUMBER = {},
PAGES = {181-216},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/angeli_deleenheer_sontag_petri_toulouse_book07.pdf}
}
@INCOLLECTION{04cime,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Nonlinear and Optimal Control Theory},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {Input to state stability: Basic concepts and results},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {P. Nistri and G. Stefani},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {163--220},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, stability,
input to state stability, nonlinear systems, detectability,
nonlinear regulation},
PDF = {../../FTPDIR/04cetraro_reprint.pdf},
ABSTRACT = { This expository presentation, prepared for a summer
course, addresses the precise formulation of questions of robustness
with respect to disturbances, using the paradigm of input to state
stability. It provides an intuitive and informal presentation of the
main concepts. }
}
@INCOLLECTION{almostmonotone_toulouse,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Biology and Control Theory: Current Challenges (Lecture Notes in Control and Information Sciences Volume 357)},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {Monotone and near-monotone systems},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {I. Queinnec and S. Tarbouriech and G. Garcia and
S-I. Niculescu},
OPTMONTH = {},
NOTE = {Conference version of ``Monotone and near-monotone biochemical networks,'' basically the same paper.},
OPTNUMBER = {},
PAGES = {79-122},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, monotone systems,
Ising spin models, nonlinear stability, dynamical systems,
consistent graphs, gene networks},
ABSTRACT = {See abstract and pdf for ``Monotone and near-monotone
biochemical networks''.}
}
@INCOLLECTION{stabilization_encyclopaedia07,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Encyclopedia of Complexity and Systems Science},
PUBLISHER = {Springer-Verlag, Berlin},
TITLE = {Stability and Feedback Stabilization},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {Robert Meyers},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTPAGES = {},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {stability, nonlinear control, feedback stabilization},
ABSTRACT = {The problem of stabilization of equilibria is one of the
central issues in control. In addition to its intrinsic interest, it
represents a first step towards the solution of more complicated
problems, such as the stabilization of periodic orbits or general
invariant sets, or the attainment of other control objectives, such
as tracking, disturbance rejection, or output feedback, all of which
may be interpreted as requiring the stabilization of some quantity
(typically, some sort of ``error'' signal). A very special case, when
there are no inputs, is that of stability. This short and informal
article provides an introduction to the subject. }
}
@INCOLLECTION{ywang_isidori_book07,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Analysis and Design of Nonlinear Control Systems},
PUBLISHER = {Springer-Verlag, London},
TITLE = {Uniformly Universal Inputs},
YEAR = {2007},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {Alessandro Astolfi},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {9-24},
OPTSERIES = {},
OPTTYPE = {},
VOLUME = {224},
KEYWORDS = {observability, identification, real-analytic functions},
PDF = {../../FTPDIR/sontag_wang_uniformly_universal08.pdf},
ABSTRACT = {A result is presented showing the existence of inputs
universal for observability, uniformly with respect to the class of
all continuous-time analytic systems. This represents an ultimate
generalization of a 1977 theorem, for bilinear systems, due to
Alberto Isidori and Osvaldo Grasselli.}
}
@ARTICLE{dasgupta-albert2,
AUTHOR = {R. Albert and B. DasGupta and R. Dondi and S. Kachalo and
E.D. Sontag and A. Zelikovsky and K. Westbrooks},
JOURNAL = {Journal of Computational Biology},
TITLE = {A novel method for signal transduction network inference
from indirect experimental evidence},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {927-949},
VOLUME = {14},
KEYWORDS = {systems biology, reaction networks, algorithms,
signal transduction networks, graph algorithms},
PDF = {../../FTPDIR/albert_dasgupta_et_all_jcb07_galleys.pdf},
ABSTRACT = {This paper introduces a new method of combined synthesis
and inference of biological signal transduction networks. The main
idea lies in representing observed causal relationships as network
paths, and using techniques from combinatorial optimization to find
the sparsest graph consistent with all experimental observations. The
paper formalizes the approach, studies its computational complexity,
proves new results for exact and approximate solutions of the
computationally hard transitive reduction substep of the approach,
validates the biological applicability by applying it to a previously
published signal transduction network by Li et al., and shows that
the algorithm for the transitive reduction substep performs well on
graphs with a structure similar to those observed in transcriptional
regulatory and signal transduction networks.}
}
@ARTICLE{persistencePetri,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
JOURNAL = {Mathematical Biosciences},
TITLE = {A Petri net approach to the study of persistence in
chemical reaction networks},
YEAR = {2007},
OPTMONTH = {},
NOTE = {Please look at the paper ``A Petri net approach to persistence analysis in chemical reaction networks'' for additional results, not included in the journal paper due to lack of space. See also the preprint: arXiv q-bio.MN/068019v2, 10 Aug 2006},
OPTNUMBER = {},
PAGES = {598-618},
VOLUME = {210},
KEYWORDS = {Petri nets, systems biology, reaction networks,
nonlinear stability, dynamical systems, futile cycles},
PDF = {../../FTPDIR/angeli_leenheer_sontag_math_biosciences_MBS-D-06-00188R1.pdf},
ABSTRACT = { Persistency is the property, for differential equations
in Rn, that solutions starting in the positive orthant do not
approach the boundary. For chemical reactions and population models,
this translates into the non-extinction property: provided that every
species is present at the start of the reaction, no species will tend
to be eliminated in the course of the reaction. This paper provides
checkable conditions for persistence of chemical species in reaction
networks, using concepts and tools from Petri net theory, and
verifies these conditions on various systems which arise in the
modeling of cell signaling pathways. }
}
@ARTICLE{berman-dasgupta-sontag-nyacad,
AUTHOR = {P. Berman and B. Dasgupta and E.D. Sontag},
JOURNAL = {Annals of the NY Academy of Sciences},
TITLE = {Algorithmic issues in reverse engineering of protein and
gene networks via the modular response analysis method},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {132-141},
VOLUME = {1115},
KEYWORDS = {systems biology, reaction networks,
gene and protein networks, reverse engineering,
systems identification, graph algorithms},
PDF = {../../FTPDIR/berman_dasgupta_sontag_modular_response_analysis_ann_ny_acad_sci_2007.pdf},
ABSTRACT = {This paper studies a computational problem motivated by
the modular response analysis method for reverse engineering of
protein and gene networks. This set-cover problem is hard to solve
exactly for large networks, but efficient approximation algorithms
are given and their complexity is analyzed.}
}
@ARTICLE{berman_dasgupta_sontag,
AUTHOR = {P. Berman and B. Dasgupta and E.D. Sontag},
JOURNAL = {Discrete Applied Mathematics Special Series on Computational Molecular Biology},
TITLE = {Randomized approximation algorithms for set multicover
problems with applications to reverse engineering of protein and gene
networks},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {733-749},
VOLUME = {155},
KEYWORDS = {systems biology, reaction networks,
gene and protein networks, systems identification,
reverse engineering},
PDF = {../../FTPDIR/dasgupta-berman-sontag-setcover-discrete-applied-math2007.pdf},
ABSTRACT = { This paper investigates computational complexity
aspects of a combinatorial problem that arises in the reverse
engineering of protein and gene networks, showing relations to an
appropriate set multicover problem with large "coverage" factor, and
providing a non-trivial analysis of a simple randomized
polynomial-time approximation algorithm for the problem. }
}
@ARTICLE{biosystems06,
AUTHOR = {B. DasGupta and G.A. Enciso and E.D. Sontag and Y. Zhang},
JOURNAL = {BioSystems},
TITLE = {Algorithmic and complexity aspects of decompositions of
biological networks into monotone subsystems},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {161-178},
VOLUME = {90},
KEYWORDS = {monotone systems, systems biology, reaction networks},
PDF = {../../FTPDIR/dasgupta_enciso_sontag_zhang_biosystems_2007.pdf},
ABSTRACT = { A useful approach to the mathematical analysis of
large-scale biological networks is based upon their decompositions
into monotone dynamical systems. This paper deals with two
computational problems associated to finding decompositions which are
optimal in an appropriate sense. In graph-theoretic language, the
problems can be recast in terms of maximal sign-consistent subgraphs.
The theoretical results include polynomial-time approximation
algorithms as well as constant-ratio inapproximability results. One
of the algorithms, which has a worst-case guarantee of 87.9% from
optimality, is based on the semidefinite programming relaxation
approach of Goemans-Williamson. The algorithm was implemented and
tested on a Drosophila segmentation network and an Epidermal Growth
Factor Receptor pathway model. }
}
@ARTICLE{gedeon05,
AUTHOR = {T. Gedeon and E.D. Sontag},
JOURNAL = {J. of Differential Equations},
TITLE = {Oscillations in multi-stable monotone systems with
slowly varying feedback},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {273-295},
VOLUME = {239},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/gedeon_sontag_JDE07.pdf},
ABSTRACT = {This paper gives a theorem showing that a slow feedback
adaptation, acting entirely analogously to the role of negative
feedback for ordinary relaxation oscillations, leads to periodic
orbits for bistable monotone systems. The proof is based upon a
combination of i/o monotone systems theory and Conley Index theory.}
}
@ARTICLE{06plos,
AUTHOR = {W. Maass and P. Joshi and E.D. Sontag},
JOURNAL = {PLoS Computational Biology},
TITLE = {Computational aspects of feedback in neural circuits},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {e165 1-20},
VOLUME = {3},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, feedback linearization,
computation by cortical microcircuits, fading memory},
PDF = {../../FTPDIR/maass_joshi_sontag_PLOS_CompBio_jan07.pdf},
ABSTRACT = { It had previously been shown that generic cortical
microcircuit models can perform complex real-time computations on
continuous input streams, provided that these computations can be
carried out with a rapidly fading memory. We investigate in this
article the computational capability of such circuits in the more
realistic case where not only readout neurons, but in addition a few
neurons within the circuit have been trained for specific tasks. This
is essentially equivalent to the case where the output of trained
readout neurons is fed back into the circuit. We show that this new
model overcomes the limitation of a rapidly fading memory. In fact,
we prove that in the idealized case without noise it can carry out
any conceivable digital or analog computation on time-varying inputs.
But even with noise the resulting computational model can perform a
large class of biologically relevant real-time computations that
require a non-fading memory. }
}
@ARTICLE{almostmonotone_journal,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems and Synthetic Biology},
TITLE = {Monotone and near-monotone biochemical networks},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {59-87},
VOLUME = {1},
KEYWORDS = {systems biology, reaction networks, monotone systems,
Ising spin models, nonlinear stability, dynamical systems,
consistent graphs, gene networks},
PDF = {../../FTPDIR/monotone_near_monotone_sontag_systems_synthetic_biology_2007.pdf},
ABSTRACT = { This paper provides an expository introduction to
monotone and near-monotone biochemical network structures. Monotone
systems respond in a predictable fashion to perturbations, and have
very robust dynamical characteristics. This makes them reliable
components of more complex networks, and suggests that natural
biological systems may have evolved to be, if not monotone, at least
close to monotone. In addition, interconnections of monotone systems
may be fruitfully analyzed using tools from control theory. },
DOI = {10.1007/s11693-007-9005-9}
}
@ARTICLE{JMathChemMonotone06,
AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag},
JOURNAL = {J. Math Chemistry},
TITLE = {Monotone chemical reaction networks},
YEAR = {2007},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {295-314},
VOLUME = {41},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/leenheer-angeli-sontag-JMathChem07.pdf},
ABSTRACT = { We analyze certain chemical reaction networks and show
that every solution converges to some steady state. The reaction
kinetics are assumed to be monotone but otherwise arbitrary. When
diffusion effects are taken into account, the conclusions remain
unchanged. The main tools used in our analysis come from the theory
of monotone dynamical systems. We review some of the features of this
theory and provide a self-contained proof of a particular
attractivity result which is used in proving our main result. },
DOI = {10.1007/s10910-006-9075-z}
}
@INPROCEEDINGS{07nolcos_persistence,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. 7th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2007), Pretoria, South Africa, 22-24 August, 2007},
TITLE = {Petri nets tools for the analysis of persistence in
chemical networks},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {Petri nets, systems biology, reaction networks,
nonlinear stability, dynamical systems, futile cycles}
}
@INPROCEEDINGS{07cdc_arcak,
AUTHOR = {M. Arcak and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007},
TITLE = {A passivity-based stability criterion for a class of
interconnected systems and applications to biochemical reaction
networks},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Conference version of journal paper with same title},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4477-4482},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks,
cyclic feedback systems, secant condition, nonlinear stability,
dynamical systems}
}
@INPROCEEDINGS{07acc_ddv,
AUTHOR = {Del Vecchio, D. and E.D. Sontag},
BOOKTITLE = {Proceedings American Control Conf., New York, July 2007},
TITLE = {Dynamics and control of synthetic bio-molecular networks},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1577-1588},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, synthetic biology},
ABSTRACT = { This tutorial paper presents an introduction to systems
and synthetic molecular biology. It provides an introduction to basic
biological concepts, and describes some of the techniques as well as
challenges in the analysis and design of biomolecular networks. }
}
@INPROCEEDINGS{07acc_jovanovic_arcak_sontag,
AUTHOR = {M.R. Jovanovic and M. Arcak and E.D. Sontag},
BOOKTITLE = {Proceedings American Control Conf., New York, July 2007},
TITLE = {Remarks on the stability of spatially distributed
systems with a cyclic interconnection structure},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2696-2701},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks,
cyclic feedback systems, spatially distributed systems,
secant condition},
ABSTRACT = { For distributed systems with a cyclic interconnection
structure, a global stability result is shown to hold if the secant
criterion is satisfied. }
}
@INPROCEEDINGS{07acc:SontagWangMegretski,
AUTHOR = {E.D. Sontag and Y. Wang and A. Megretski},
BOOKTITLE = {Proceedings American Control Conf., New York, July 2007},
TITLE = {Remarks on Input Classes for Identification of Bilinear
Systems},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4345-4350},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {realization theory, observability, identifiability,
bilinear systems}
}
@INPROCEEDINGS{07cdc_WS,
AUTHOR = {L. Wang and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 2007},
TITLE = {Further results on singularly perturbed monotone
systems, with an application to double phosphorylation cycles},
YEAR = {2007},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Conference version of Singularly perturbed monotone systems and an application to double phosphorylation cycles.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {627-632},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {singular perturbations, futile cycles, MAPK cascades,
systems biology, reaction networks, nonlinear stability,
nonlinear dynamics, multistability, monotone systems}
}
@INCOLLECTION{dasgupta-book05,
AUTHOR = {B. Dasgupta and P. Berman and E.D. Sontag},
BOOKTITLE = {Advances in Computational Intelligence: Theory & Applications},
PUBLISHER = {World Scientific, Hackensack},
TITLE = {Computational complexities of combinatorial problems
with applications to reverse engineering of biological networks},
YEAR = {2006},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {D. Liu and F-Y. Wan},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {303--316},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks,
gene and protein networks, reverse engineering,
systems identification, theory of computing and complexity}
}
@INCOLLECTION{dasgupta_enciso05,
AUTHOR = {B. Dasgupta and G.A. Enciso and E.D. Sontag and Y. Zhang},
BOOKTITLE = {Lecture Notes in Computer Science: Experimental Algorithms: 5th International Workshop, WEA 2006},
PUBLISHER = {Springer-Verlag},
TITLE = {Algorithmic and complexity results for decompositions of
biological networks into monotone subsystems},
YEAR = {2006},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C. lvarez and M. Serna},
OPTMONTH = {},
NOTE = {(Cala Galdana, Menorca, Spain, May 24-27, 2006)},
OPTNUMBER = {},
PAGES = {253--264},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, monotone systems,
theory of computing and complexity}
}
@INCOLLECTION{05nips,
AUTHOR = {W. Maass and P. Joshi and E.D. Sontag},
BOOKTITLE = {Advances in Neural Information Processing Systems 18},
PUBLISHER = {MIT Press, Cambridge},
TITLE = {Principles of real-time computing with feedback applied
to cortical microcircuit models},
YEAR = {2006},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-18, Vancouver 2005, https://proceedings.neurips.cc/paper/2005},
OPTNUMBER = {},
OPTPAGES = {},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/05nips_maass_joshi_sontag.pdf},
ABSTRACT = {The network topology of neurons in the brain exhibits an
abundance of feedback connections, but the computational function of
these feedback connections is largely unknown. We present a
computational theory that characterizes the gain in computational
power achieved through feedback in dynamical systems with fading
memory. It implies that many such systems acquire through feedback
universal computational capabilities for analog computing with a
non-fading memory. In particular, we show that feedback enables such
systems to process time-varying input streams in diverse ways
according to rules that are implemented through internal states of
the dynamical system. In contrast to previous attractor-based
computational models for neural networks, these flexible internal
states are high-dimensional attractors of the circuit dynamics, that
still allow the circuit state to absorb new information from online
input streams. In this way one arrives at novel models for working
memory, integration of evidence, and reward expectation in cortical
circuits. We show that they are applicable to circuits of
conductance-based Hodgkin-Huxley (HH) neurons with high levels of
noise that reflect experimental data on invivo conditions.}
}
@ARTICLE{arcak_secant,
AUTHOR = {M. Arcak and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Diagonal stability of a class of cyclic systems and its
connection with the secant criterion},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1531-1537},
VOLUME = {42},
KEYWORDS = {passive systems, systems biology, reaction networks,
cyclic feedback systems, secant condition, nonlinear stability,
dynamical systems},
PDF = {../../FTPDIR/arcak_sontag_automatica06.pdf},
ABSTRACT = { This paper considers a class of systems with a cyclic
structure that arises, among other examples, in dynamic models for
certain biochemical reactions. We first show that a criterion for
local stability, derived earlier in the literature, is in fact a
necessary and sufficient condition for diagonal stability of the
corresponding class of matrices. We then revisit a recent
generalization of this criterion to output strictly passive systems,
and recover the same stability condition using our diagonal stability
result as a tool for constructing a Lyapunov function. Using this
procedure for Lyapunov construction we exhibit classes of cyclic
systems with sector nonlinearities and characterize their global
stability properties. }
}
@ARTICLE{chaves_automatica06,
AUTHOR = {M. Chaves and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Exact computation of amplification for a class of
nonlinear systems arising from cellular signaling pathways},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1987-1992},
VOLUME = {42},
KEYWORDS = {MAPK cascades, systems biology, reaction networks,
nonlinear stability, dynamical systems},
PDF = {../../FTPDIR/chaves_gains_comparison_automatica06.pdf},
ABSTRACT = { A commonly employed measure of the signal amplification
properties of an input/output system is its induced L2 norm,
sometimes also known as H-infinity gain. In general, however, it is
extremely difficult to compute the numerical value for this norm, or
even to check that it is finite, unless the system being studied is
linear. This paper describes a class of systems for which it is
possible to reduce this computation to that of finding the norm of an
associated linear system. In contrast to linearization approaches, a
precise value, not an estimate, is obtained for the full nonlinear
model. The class of systems that we study arose from the modeling of
certain biological intracellular signaling cascades, but the results
should be of wider applicability. }
}
@ARTICLE{csa06,
AUTHOR = {M. Chaves and E.D. Sontag and R. Albert},
JOURNAL = {IET Systems Biology},
TITLE = {Methods of robustness analysis for Boolean models of
gene control networks},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {154-167},
VOLUME = {153},
KEYWORDS = {systems biology, reaction networks, boolean systems,
identifiability, robust, robustness, geometry, Boolean,
segment polarity network, gene and protein networks, hybrid systems},
PDF = {../../FTPDIR/chaves_sontag_albert_sysbio_2006.pdf},
ABSTRACT = { As a discrete approach to genetic regulatory networks,
Boolean models provide an essential qualitative description of the
structure of interactions among genes and proteins. Boolean models
generally assume only two possible states (expressed or not
expressed) for each gene or protein in the network as well as a high
level of synchronization among the various regulatory processes. In
this paper, we discuss and compare two possible methods of adapting
qualitative models to incorporate the continuous-time character of
regulatory networks. The first method consists of introducing
asynchronous updates in the Boolean model. In the second method, we
adopt the approach introduced by L. Glass to obtain a set of
piecewise linear differential equations which continuously describe
the states of each gene or protein in the network. We apply both
methods to a particular example: a Boolean model of the segment
polarity gene network of Drosophila melanogaster. We analyze the
dynamics of the model, and provide a theoretical characterization of
the model's gene pattern prediction as a function of the timescales
of the various processes. }
}
@ARTICLE{bdas00,
AUTHOR = {B. DasGupta and J.P. Hespanha and J. Riehl and
E.D. Sontag},
JOURNAL = {Nonlinear Analysis},
TITLE = {Honey-pot constrained searching with local sensory
information},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1773-1793},
VOLUME = {65},
KEYWORDS = {search problems, algorithms, computational complexity},
PDF = {../../FTPDIR/dasgupta_hespanha_riehl_sontag_nonlinearanalysis06.pdf},
ABSTRACT = { This paper investigates the problem of searching for a
hidden target in a bounded region of the plane by an autonomous robot
which is only able to use limited local sensory information. It
proposes an aggregation-based approach to solve this problem, in
which the continuous search space is partitioned into a finite
collection of regions on which we define a discrete search problem
and a solution to the original problem is obtained through a
refinement procedure that lifts the discrete path into a continuous
one. The resulting solution is in general not optimal but one can
construct bounds to gauge the cost penalty incurred. The discrete
version is formalized and an optimization problem is stated as a
`reward-collecting' bounded-length path problem. NP-completeness and
efficient approximation algorithms for various cases of this problem
are discussed. }
}
@ARTICLE{enciso_smith_sontagJDE06,
AUTHOR = {G.A. Enciso and H.L. Smith and E.D. Sontag},
JOURNAL = {J. of Differential Equations},
TITLE = {Non-monotone systems decomposable into monotone systems
with negative feedback},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {205-227},
VOLUME = {224},
KEYWORDS = {nonlinear stability, dynamical systems,
monotone systems},
PDF = {../../FTPDIR/enciso_smith_sontag_JDE06.pdf},
ABSTRACT = { Motivated by the theory of monotone i/o systems, this
paper shows that certain finite and infinite dimensional
semi-dynamical systems with negative feedback can be decomposed into
a monotone open loop system with inputs and a decreasing output
function. The original system is reconstituted by plugging the output
into the input. By embedding the system into a larger symmetric
monotone system, this paper obtains finer information on the
asymptotic behavior of solutions, including existence of positively
invariant sets and global convergence. An important new result is the
extension of the "small gain theorem" of monotone i/o theory to
reaction-diffusion partial differential equations: adding diffusion
preserves the global attraction of the ODE equilibrium. }
}
@ARTICLE{dcds06,
AUTHOR = {G.A. Enciso and E.D. Sontag},
JOURNAL = {Discrete Contin. Dyn. Syst.},
TITLE = {Global attractivity, I/O monotone small-gain theorems,
and biological delay systems},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {549--578},
VOLUME = {14},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems, delay-differential systems},
PDF = {../../FTPDIR/enciso_sontag_DCDS06_galleys.pdf},
ABSTRACT = { This paper further develops a method, originally
introduced in a paper by Angeli and Sontag, for proving global
attractivity of steady states in certain classes of dynamical
systems. In this aproach, one views the given system as a negative
feedback loop of a monotone controlled system. An auxiliary discrete
system, whose global attractivity implies that of the original
system, plays a key role in the theory, which is presented in a
general Banach space setting. Applications are given to delay
systems, as well as to systems with multiple inputs and outputs, and
the question of expressing a given system in the required negative
feedback form is addressed. }
}
@ARTICLE{malisoff-krichman-sontag,
AUTHOR = {M. Malisoff and M. Krichman and E.D. Sontag},
JOURNAL = {Journal of Dynamical and Control Systems},
TITLE = {Global stabilization for systems evolving on manifolds},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {161--184},
VOLUME = {12},
KEYWORDS = {nonlinear stability, nonlinear control,
feedback stabilization},
PDF = {../../FTPDIR/malisoff-krichman-sontag-JCDS06.pdf},
ABSTRACT = { This paper shows that any globally asymptotically
controllable system on any smooth manifold can be globally stabilized
by a state feedback. Since discontinuous feedbacks are allowed,
solutions are understood in the ``sample and hold'' sense introduced
by Clarke-Ledyaev-Sontag-Subbotin (CLSS). This work generalizes the
CLSS Theorem, which is the special case of our result for systems on
Euclidean space. We apply our result to the input-to-state
stabilization of systems on manifolds relative to actuator errors,
under small observation noise. }
}
@ARTICLE{ryan05,
AUTHOR = {E.P. Ryan and E.D. Sontag},
JOURNAL = {Systems and Control Letters},
TITLE = {Well-defined steady-state response does not imply CICS},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {707-710},
VOLUME = {55},
KEYWORDS = {nonlinear stability, dynamical systems},
PDF = {../../FTPDIR/ryan-sontag-SCL06.pdf},
ABSTRACT = { Systems for which each constant input gives rise to a
unique globally attracting equilibrium are considered. A
counterexample is provided to show that inputs which are only
asymptotically constant may not result in states converging to
equilibria (failure of the converging-input converging state, or
``CICS'' property). },
DOI = {10.1016/j.sysconle.2006.02.001}
}
@ARTICLE{secant,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Passivity gains and the ``secant condition'' for
stability},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {177--183},
VOLUME = {55},
KEYWORDS = {cyclic feedback systems, systems biology,
reaction networks, nonlinear stability, dynamical systems,
passive systems, secant condition, reaction networks},
PDF = {../../FTPDIR/secant_SCL06.pdf},
ABSTRACT = { A generalization of the classical secant condition for
the stability of cascades of scalar linear systems is provided for
passive systems. The key is the introduction of a quantity that
combines gain and phase information for each system in the cascade.
For linear one-dimensional systems, the known result is recovered
exactly. }
}
@ARTICLE{ywang_cooperative_example,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {J. of Differential Equations},
TITLE = {A cooperative system which does not satisfy the limit
set dichotomy},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {373-384},
VOLUME = {224},
KEYWORDS = {dynamical systems, monotone systems},
PDF = {../../FTPDIR/sontag_ywang_JDE_2006.pdf},
ABSTRACT = { The fundamental property of strongly monotone systems,
and strongly cooperative systems in particular, is the limit set
dichotomy due to Hirsch: if x < y, then either Omega(x) < Omega (y),
or Omega(x) = Omega(y) and both sets consist of equilibria. We
provide here a counterexample showing that this property need not
hold for (non-strongly) cooperative systems. }
}
@ARTICLE{crowding,
AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag},
JOURNAL = {Journal of Mathematical Analysis and Applications},
TITLE = {Crowding effects promote coexistence in the chemostat},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {48-60},
VOLUME = {319},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/leenheer_angeli_sontag_JMAA06.pdf},
ABSTRACT = { We provide an almost-global stability result for a
particular chemostat model, in which crowding effects are taken into
consideration. The model can be rewritten as a negative feedback
interconnection of two monotone i/o systems with well-defined
characteristics, which allows the use of a small-gain theorem for
feedback interconnections of monotone systems. This leads to a
sufficient condition for almost-global stability, and we show that
coexistence occurs in this model if the crowding effects are large
enough. }
}
@ARTICLE{leenheer-levin-klausmeier,
AUTHOR = {de Leenheer, P. and S.A. Levin and E.D. Sontag and
C.A. Klausmeier},
JOURNAL = {J. Mathematical Biology},
TITLE = {Global stability in a chemostat with multiple nutrients},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {419--438},
VOLUME = {52},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/leenheer_levin_sontag_klausmeier_JMB06.pdf},
ABSTRACT = { We study a single species in a chemostat, limited by
two nutrients, and separate nutrient uptake from growth. For a broad
class of uptake and growth functions it is proved that a nontrivial
equilibrium may exist. Moreover, if it exists it is unique and
globally stable, generalizing a previous result by Legovic and
Cruzado. }
}
@ARTICLE{vanriel06,
AUTHOR = {van Riel, N.A.W. and E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {Parameter estimation in models combining signal
transduction and metabolic pathways: The dependent input approach},
YEAR = {2006},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {263-274},
VOLUME = {153},
KEYWORDS = {systems biology, reaction networks,
parameter identification},
PDF = {../../FTPDIR/vanriel_sontag_sysbio_153_pp_263_274_2006.pdf},
ABSTRACT = { Biological complexity and limited quantitative
measurements impose severe challenges to standard engineering
methodologies for systems identification. This paper presents an
approach, justified by the theory of universal inputs for
distinguishability, based on replacing unmodeled dynamics by
fictitious `dependent inputs'. The approach is particularly useful in
validation experiments, because it allows one to fit model parameters
to experimental data generated by a reference (wild-type) organism
and then testing this model on data generated by a variation
(mutant), so long as the mutations only affect the unmodeled dynamics
that produce the dependent inputs. As a case study, this paper
addresses the pathways that control the nitrogen uptake fluxes in
baker's yeast Saccharomyces cerevisiae enabling it to optimally
respond to changes in nitrogen availability. Well-defined
perturbation experiments were performed on cells growing in
steady-state. Time-series data of extracellular and intracellular
metabolites were obtained, as well as mRNA levels. A nonlinear model
was proposed, and shown to be structurally identifiable given
input/output data. The identified model correctly predicted the
responses of different yeast strains and different perturbations. }
}
@INPROCEEDINGS{06cdc_iglesias-andrews,
AUTHOR = {B. Andrews and P. Iglesias and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006},
TITLE = {Signal detection and approximate adaptation implies an
approximate internal model},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2364-2369},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {biological adaptation, internal model principle},
PDF = {../../FTPDIR/06cdc_burton_iglesias_sontag_final.pdf},
ABSTRACT = { This conference paper presented a version of an
approximate internal model principle, for linear systems. A
subsequent paper at the IFAC 2008 conference improved on this result
by extending it to a class of nonlinear systems. }
}
@INPROCEEDINGS{translation-inv-med06,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Control and Automation, 2006. MED '06. 14th Mediterranean Conference on, 28-30 June 2006},
TITLE = {A note on monotone systems with positive translation
invariance},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {available from ieeexplore.ieee.org},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1-6},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli_translation_invariance_med06.pdf},
ABSTRACT = { Strongly monotone systems of ordinary differential
equations which have a certain translation-invariance property are
shown to have the property that all projected solutions converge to a
unique equilibrium. This result may be seen as a dual of a well-known
theorem of Mierczynski for systems that satisfy a conservation law.
As an application, it is shown that enzymatic futile cycles have a
global convergence property. },
DOI = {10.1109/MED.2006.3287822B2B2B2B2B2B}
}
@INPROCEEDINGS{06cdc_chemical,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006},
TITLE = {On the structural monotonicity of chemical reaction
networks},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {7-12},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {monotone systems, systems biology, reaction networks,
nonlinear stability, dynamical systems},
PDF = {../../FTPDIR/06cdc_angeli_leenheer_sontag_final.pdf},
ABSTRACT = { This paper derives new results for certain classes of
chemical reaction networks, linking structural to dynamical
properties. In particular, it investigates their monotonicity and
convergence without making assumptions on the structure (e.g.,
mass-action kinetics) of the dynamical equations involved, and
relying only on stoichiometric constraints. The key idea is to find a
suitable set of coordinates under which the resulting system is
cooperative. As a simple example, the paper shows that a
phosphorylation/dephosphorylation process, which is involved in many
signaling cascades, has a global stability property. }
}
@INPROCEEDINGS{arcak-06acc,
AUTHOR = {M. Arcak and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conference, Minneapolis, June 2006},
TITLE = {Connections between diagonal stability and the secant
condition for cyclic systems},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1493-1498},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks,
cyclic feedback systems, secant condition, nonlinear stability,
dynamical systems}
}
@INPROCEEDINGS{06cdc_chaves-albert,
AUTHOR = {M. Chaves and E.D. Sontag and R. Albert},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006},
TITLE = {Structure and timescale analysis in genetic regulatory
networks},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2358-2363},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {genetic regulatory networks, Boolean systems,
hybrid systems},
PDF = {../../FTPDIR/06cdc_chaves_albert_sontag_final.pdf},
ABSTRACT = { This work is concerned with the study of the robustness
and fragility of gene regulation networks to variability in the
timescales of the distinct biological processes involved. It explores
and compares two methods: introducing asynchronous updates in a
Boolean model, or integrating the Boolean rules in a continuous,
piecewise linear model. As an example, the segment polarity network
of the fruit fly is analyzed. A theoretical characterization is given
of the model's ability to predict the correct development of the
segmented embryo, in terms of the specific timescales of the various
regulation interactions. }
}
@INPROCEEDINGS{06cdc_wang_sontag,
AUTHOR = {L. Wang and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Diego, Dec. 2006},
TITLE = {A remark on singular perturbations of strongly monotone
systems},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {989-994},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, singular perturbations, monotone systems},
PDF = {../../FTPDIR/06cdc_limingwang_sontag_final.pdf},
ABSTRACT = { This paper deals with global convergence to equilibria,
and in particular Hirsch's generic convergence theorem for strongly
monotone systems, for singular perturbations of monotone systems. }
}
@INPROCEEDINGS{06posta_wang,
AUTHOR = {L. Wang and E.D. Sontag},
BOOKTITLE = {Positive Systems},
TITLE = {Almost global convergence in singular perturbations of
strongly monotone systems},
YEAR = {2006},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {C. Commault and N. Marchand},
OPTMONTH = {},
NOTE = {(Lecture Notes in Control and Information Sciences Volume 341, Proceedings of the second Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 06) Grenoble, France)},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {415--422},
PUBLISHER = {Springer-Verlag, Berlin/Heidelberg},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, singular perturbations, monotone systems},
PDF = {../../FTPDIR/wang-sontag_posta06_published.pdf},
ABSTRACT = { This paper deals with global convergence to equilibria,
and in particular Hirsch's generic convergence theorem for strongly
monotone systems, for singular perturbations of monotone systems. },
DOI = {10.1007/3-540-34774-7}
}
@ARTICLE{kholodenkoJTB05,
AUTHOR = {M. Andrec and B.N. Kholodenko and R.M. Levy and
E.D. Sontag},
JOURNAL = {J. Theoret. Biol.},
TITLE = {Inference of signaling and gene regulatory networks by
steady-state perturbation experiments: structure and accuracy},
YEAR = {2005},
OPTMONTH = {},
NOTE = {Supplementary materials are here: http://sontaglab.org/FTPDIR/andrec-kholodenko-levy-sontag-JTB04-supplementary.pdf},
NUMBER = {3},
PAGES = {427--441},
VOLUME = {232},
KEYWORDS = {systems biology, reaction networks,
gene and protein networks, systems identification,
reverse engineering, modular response analysis, systems biology,
reaction networks, reverse engineering, gene and protein networks,
protein networks, gene networks, systems identification},
PDF = {../../FTPDIR/andrec_kholodenko_levy_sontag_JTB04.pdf},
ABSTRACT = { One of the fundamental problems of cell biology is the
understanding of complex regulatory networks. Such networks are
ubiquitous in cells, and knowledge of their properties is essential
for the understanding of cellular behavior. This paper studies the
effect of experimental uncertainty on the accuracy of the inferred
structure of the networks determined using the method in "Untangling
the wires: a novel strategy to trace functional interactions in
signaling and gene networks". }
}
@ARTICLE{chaves_albert_sontagJTB05,
AUTHOR = {M. Chaves and R. Albert and E.D. Sontag},
JOURNAL = {J. Theoret. Biol.},
TITLE = {Robustness and fragility of Boolean models for genetic
regulatory networks},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {431--449},
VOLUME = {235},
KEYWORDS = {systems biology, reaction networks, boolean systems,
gene and protein networks},
PDF = {../../FTPDIR/chaves_albert_sontag_JTB05.pdf},
ABSTRACT = { Interactions between genes and gene products give rise
to complex circuits that enable cells to process information and
respond to external signals. Theoretical studies often describe these
interactions using continuous, stochastic, or logical approaches.
Here we propose a framework for gene regulatory networks that
combines the intuitive appeal of a qualitative description of gene
states with a high flexibility in incorporating stochasticity in the
duration of cellular processes. We apply our methods to the
regulatory network of the segment polarity genes, thus gaining novel
insights into the development of gene expression patterns. For
example, we show that very short synthesis and decay times can
perturb the wild type pattern. On the other hand, separation of
timescales between pre- and post-translational processes and a
minimal prepattern ensure convergence to the wild type expression
pattern regardless of fluctuations. }
}
@ARTICLE{enciso_sontagSCL05,
AUTHOR = {G.A. Enciso and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Monotone systems under positive feedback: multistability
and a reduction theorem},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {159--168},
VOLUME = {54},
KEYWORDS = {multistability, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems},
PDF = {../../FTPDIR/enciso_sontag_multistability_SCL04_inpress.pdf},
ABSTRACT = { For feedback loops involving single input, single
output monotone systems with well-defined I/O characteristics, a
previous paper provided an approach to determining the location and
stability of steady states. A result on global convergence for
multistable systems followed as a consequence of the technique. The
present paper extends the approach to multiple inputs and outputs. A
key idea is the introduction of a reduced system which preserves
local stability properties. New results characterizing strong
monotonicity of feedback loops involving cascades are also presented. }
}
@ARTICLE{HLAS,
AUTHOR = {J.P. Hespanha and D. Liberzon and D. Angeli and
E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Nonlinear norm-observability notions and stability of
switched systems},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {154--168},
VOLUME = {50},
KEYWORDS = {observability, input to state stability, observability,
invariance principle},
PDF = {../../FTPDIR/liberzon-hespanha-angeli-sontag-observability-TAC05.pdf},
ABSTRACT = { This paper proposes several definitions of
observability for nonlinear systems and explores relationships among
them. These observability properties involve the existence of a bound
on the norm of the state in terms of the norms of the output and the
input on some time interval. A Lyapunov-like sufficient condition for
observability is also obtained. As an application, we prove several
variants of LaSalle's stability theorem for switched nonlinear
systems. These results are demonstrated to be useful for control
design in the presence of switching as well as for developing
stability results of Popov type for switched feedback systems. }
}
@ARTICLE{mancilla_garcia_wang_representation05,
AUTHOR = {J. L. Mancilla-Aguilar and R. Garca and E.D. Sontag and
Y. Wang},
JOURNAL = {Nonlinear Anal.},
TITLE = {On the representation of switched systems with inputs by
perturbed control systems},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1111--1150},
VOLUME = {60},
PDF = {../../FTPDIR/mancilla-garcia-wang-sontag-switched-representations-NA05.pdf},
ABSTRACT = { This paper provides representations of switched systems
described by controlled differential inclusions, in terms of
perturbed control systems. The control systems have dynamics given by
differential equations, and their inputs consist of the original
controls together with disturbances that evolve in compact sets;
their sets of maximal trajectories contain, as a dense subset, the
set of maximal trajectories of the original system. Several
applications to control theory, dealing with properties of stability
with respect to inputs and of detectability, are derived as a
consequence of the representation theorem. }
}
@ARTICLE{mancilla-garcia-wang-representation-switches,
AUTHOR = {J. L. Mancilla-Aguilar and R. Garca and E.D. Sontag and
Y. Wang},
JOURNAL = {Nonlinear Anal.},
TITLE = {Uniform stability properties of switched systems with
switchings governed by digraphs},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {472--490},
VOLUME = {63},
PDF = {../../FTPDIR/mancilla_garcia_sontag_wang_switching-diagraph_NA05.pdf},
ABSTRACT = { This paper develops characterizations of various
uniform stability properties of switched systems described by
differential inclusions, and whose switchings are governed by a
digraph. These characterizations are given in terms of stability
properties of the system with restricted switchings and also in terms
of Lyapunov functions. }
}
@ARTICLE{ejc05es,
AUTHOR = {E.D. Sontag},
JOURNAL = {Eur. J. Control},
TITLE = {Molecular systems biology and control},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4-5},
PAGES = {396--435},
VOLUME = {11},
KEYWORDS = {cell biology, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems,
molecular biology, systems biology, cellular signaling},
PDF = {../../FTPDIR/05cdc_ejc_oct05.pdf},
ABSTRACT = { This paper, prepared for a tutorial at the 2005 IEEE
Conference on Decision and Control, presents an introduction to
molecular systems biology and some associated problems in control
theory. It provides an introduction to basic biological concepts,
describes several questions in dynamics and control that arise in the
field, and argues that new theoretical problems arise naturally in
this context. A final section focuses on the combined use of
graph-theoretic, qualitative knowledge about monotone building-blocks
and steady-state step responses for components. }
}
@ARTICLE{predatorpreysgt05,
AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag},
JOURNAL = {Math. Biosci. Eng.},
TITLE = {On predator-prey systems and small-gain theorems},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {25--42},
VOLUME = {2},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli-leenheer-sontag-MBE04.pdf},
ABSTRACT = { This paper deals with an almost global attractivity
result for Lotka-Volterra systems with predator-prey interactions.
These systems can be written as (negative) feedback systems. The
subsystems of the feedback loop are monotone control systems,
possessing particular input-output properties. We use a small-gain
theorem, adapted to a context of systems with multiple equilibrium
points to obtain the desired almost global attractivity result. It
provides sufficient conditions to rule out oscillatory or more
complicated behavior which is often observed in predator-prey
systems. }
}
@INPROCEEDINGS{05cdc_enciso_sontag,
AUTHOR = {G.A. Enciso and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications},
TITLE = {A remark on multistability for monotone systems II},
YEAR = {2005},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2957--2962},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {multistability, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems}
}
@INPROCEEDINGS{05cdc-secant,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Seville, Dec. 2005, IEEE Publications},
TITLE = {A notion of passivity gain and a generalization of the
`secant condition' for stability},
YEAR = {2005},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {5645--5649},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {nonlinear stability, dynamical systems}
}
@INPROCEEDINGS{05ifac,
AUTHOR = {E.D. Sontag and M. Chaves},
BOOKTITLE = {Proc. 16th IFAC World Congress, Prague, July 2005},
TITLE = {Computation of amplification for systems arising from
cellular signaling pathways},
YEAR = {2005},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, dynamical systems}
}
@INCOLLECTION{monotoneLSU,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Optimal control, stabilization and nonsmooth analysis},
PUBLISHER = {Springer},
TITLE = {Interconnections of monotone systems with steady-state
characteristics},
YEAR = {2004},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {135--154},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {301},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/monotone_lsu_book_springer2004.pdf},
ABSTRACT = { One of the key ideas in control theory is that of
viewing a complex dynamical system as an interconnection of simpler
subsystems, thus deriving conclusions regarding the complete system
from properties of its building blocks. Following this paradigm, and
motivated by questions in molecular biology modeling, the authors
have recently developed an approach based on components which are
monotone systems with respect to partial orders in state and signal
spaces. This paper presents a brief exposition of recent results,
with an emphasis on small gain theorems for negative feedback, and
the emergence of multistability and associated hysteresis effects
under positive feedback. }
}
@INCOLLECTION{MalisoffSontag04,
AUTHOR = {M. Malisoff and E.D. Sontag},
BOOKTITLE = {Optimal control, stabilization and nonsmooth analysis},
PUBLISHER = {Springer},
TITLE = {Asymptotic controllability and input-to-state
stabilization: the effect of actuator errors},
YEAR = {2004},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {155--171},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {301},
KEYWORDS = {input to state stability, control-Lyapunov functions,
nonlinear control, feedback stabilization, ISS},
PDF = {../../FTPDIR/malisoff_sontag_lsu_springer2004.pdf},
ABSTRACT = { We discuss several issues related to the
stabilizability of nonlinear systems. First, for continuously
stabilizable systems, we review constructions of feedbacks that
render the system input-to-state stable with respect to actuator
errors. Then, we discuss a recent paper which provides a new feedback
design that makes globally asymptotically controllable systems
input-to-state stable to actuator errors and small observation noise.
We illustrate our constructions using the nonholonomic integrator,
and discuss a related feedback design for systems with disturbances. }
}
@ARTICLE{pnasangeliferrellsontag04,
AUTHOR = {D. Angeli and J. E. Ferrell and E.D. Sontag},
JOURNAL = {Proc Natl Acad Sci USA},
TITLE = {Detection of multistability, bifurcations, and
hysteresis in a large class of biological positive-feedback systems.},
YEAR = {2004},
OPTMONTH = {},
NOTE = {A revision of Suppl. Fig. 7(b) is here: http://sontaglab.org/FTPDIR/nullclines-f-g-REV.jpg; and typos can be found here: http://sontaglab.org/FTPDIR/angeli-ferrell-sontag-pnas04-errata.txt},
NUMBER = {7},
PAGES = {1822--1827},
VOLUME = {101},
KEYWORDS = {MAPK cascades, multistability, systems biology,
reaction networks, nonlinear stability, dynamical systems,
monotone systems},
URL = {http://dx.doi.org/10.1073/pnas.0308265100},
PDF = {../../FTPDIR/angeli_ferrell_sontag_pnas04_paper_and_supplementary.pdf},
ABSTRACT = { Multistability is an important recurring theme in cell
signaling, of particular relevance to biological systems that switch
between discrete states, generate oscillatory responses, or
"remember" transitory stimuli. Standard mathematical methods allow
the detection of bistability in some very simple feedback systems
(systems with one or two proteins or genes that either activate each
other or inhibit each other), but realistic depictions of signal
transduction networks are invariably much more complex than this.
Here we show that for a class of feedback systems of arbitrary order,
the stability properties of the system can be deduced mathematically
from how the system behaves when feedback is blocked. Provided that
this "open loop," feedback-blocked system is monotone and possesses a
sigmoidal characteristic, the system is guaranteed to be bistable for
some range of feedback strengths. We present a simple graphical
method for deducing the stability behavior and bifurcation diagrams
for such systems, and illustrate the method with two examples taken
from recent experimental studies of bistable systems: a two-variable
Cdc2/Wee1 system and a more complicated five-variable MAPK cascade. },
DOI = {10.1073/pnas.0308265100}
}
@ARTICLE{angeli_ingalls_sontag_wang_separation_SICOPT04,
AUTHOR = {D. Angeli and B.P. Ingalls and E.D. Sontag and Y. Wang},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Separation principles for input-output and
integral-input-to-state stability},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {256--276},
VOLUME = {43},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
input to output stability},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/separation_principles_ios_iiss_angeli_ingalls_sontag_wang_SICON04.pdf},
ABSTRACT = { We present new characterizations of
input-output-to-state stability. This is a notion of detectability
formulated in the ISS framework. Equivalent properties are presented
in terms of asymptotic estimates of the state trajectories based on
the magnitudes of the external input and output signals. These
results provide a set of "separation principles" for
input-output-to-state stability , characterizations of the property
in terms of weaker stability notions. When applied to the closely
related notion of integral ISS, these characterizations yield
analogous results. },
DOI = {http://dx.doi.org/10.1137/S0363012902419047}
}
@ARTICLE{angeli_ingalls_sontag_wang_UGAS_DE_DynCtrSys04,
AUTHOR = {D. Angeli and B.P. Ingalls and E.D. Sontag and Y. Wang},
JOURNAL = {J. Dynam. Control Systems},
TITLE = {Uniform global asymptotic stability of differential
inclusions},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {391--412},
VOLUME = {10},
ADDRESS = {Hingham, MA, USA},
KEYWORDS = {differential inclusions},
PUBLISHER = {Kluwer Academic Publishers},
PDF = {../../FTPDIR/ingalls-ywang-angeli-sontag-gas-ugas-di-JDCS04.pdf},
ABSTRACT = { The stability of differential inclusions defined by
locally Lipschitz compact valued maps is addressed. It is shown that
if such a differential inclusion is globally asymptotically stable,
then in fact it is uniformly globally asymptotically stable (with
respect to initial states in compacts). This statement is trivial for
differential equations, but here we provide the extension to compact
(not necessarily convex) valued differential inclusions. The main
result is presented in a context which is useful for
control-theoretic applications: a differential inclusion with two
outputs is considered, and the result applies to the property of
global error detectability. },
DOI = {http://dx.doi.org/10.1023/B:JODS.0000034437.54937.7f}
}
@ARTICLE{monotoneMulti,
AUTHOR = {D. Angeli and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Multi-stability in monotone input/output systems},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3-4},
PAGES = {185--202},
VOLUME = {51},
KEYWORDS = {multistability, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli_sontag_multistability_SCL04.pdf},
ABSTRACT = { This paper studies the emergence of multistability and
hysteresis in those systems that arise, under positive feedback, from
monotone systems with well-defined steady-state responses. Such
feedback configurations appear routinely in several fields of
application, and especially in biology. The results are stated in
terms of directly checkable conditions which do not involve explicit
knowledge of basins of attractions of each equilibria. }
}
@ARTICLE{angelileenheersontagSCL04,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A small-gain theorem for almost global convergence of
monotone systems},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {407--414},
VOLUME = {52},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli_leenheer_sontag_SCL04.pdf},
ABSTRACT = { A small-gain theorem is presented for almost global
stability of monotone control systems which are open-loop almost
globally stable, when constant inputs are applied. The theorem
assumes "negative feedback" interconnections. This typically destroys
the monotonicity of the original flow and potentially destabilizes
the resulting closed-loop system. }
}
@ARTICLE{signaling_gains04,
AUTHOR = {M. Chaves and R.J. Dinerstein and E.D. Sontag},
JOURNAL = {J. Physical Chemistry},
TITLE = {Optimal length and signal amplification in weakly
activated signal transduction cascades},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {15311--15320},
VOLUME = {108},
KEYWORDS = {systems biology, reaction networks, dynamical systems},
PDF = {../../FTPDIR/chaves-sontag-dinerstein-signaling-gains-JPC-with-supplement.pdf},
ABSTRACT = { Weakly activated signaling cascades can be modeled as
linear systems. The input-to-output transfer function and the
internal gain of a linear system, provide natural measures for the
propagation of the input signal down the cascade and for the
characterization of the final outcome. The most efficient design of a
cascade for generating sharp signals, is obtained by choosing all the
off rates equal, and a "universal" finite optimal length. }
}
@ARTICLE{receptorligandJTB04,
AUTHOR = {M. Chaves and E.D. Sontag and R. J. Dinerstein},
JOURNAL = {J. Theoret. Biol.},
TITLE = {Steady-states of receptor-ligand dynamics: A theoretical
framework},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {413--428},
VOLUME = {227},
KEYWORDS = {zero-deficiency networks, systems biology,
reaction networks, receptor-ligand models, dynamical systems},
PDF = {../../FTPDIR/chaves-sontag-dinerstein-JTB04.pdf},
ABSTRACT = { This paper studies aspects of the dynamics of a
conventional mechanism of ligand-receptor interactions, with a focus
on the stability and location of steady-states. A theoretical
framework is developed, and, as an application, a minimal
parametrization is provided for models for two- or multi-state
receptor interaction with ligand. In addition, an "affinity quotient"
is introduced, which allows an elegant classification of ligands into
agonists, neutral agonists, and inverse agonists. }
}
@ARTICLE{testosterone,
AUTHOR = {G.A. Enciso and E.D. Sontag},
JOURNAL = {J. Math. Biol.},
TITLE = {On the stability of a model of testosterone dynamics},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {627--634},
VOLUME = {49},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems, delay-differential systems},
PDF = {../../FTPDIR/enciso-sontag-testosterone-JMB.pdf},
ABSTRACT = { We prove the global asymptotic stability of a
well-known delayed negative-feedback model of testosterone dynamics,
which has been proposed as a model of oscillatory behavior. We
establish stability (and hence the impossibility of oscillations)
even in the presence of delays of arbitrary length. }
}
@ARTICLE{kuusela_ocone_sontag04,
AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Learning Complexity Dimensions for a Continuous-Time
Control System},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {872--898},
VOLUME = {43},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {machine learning, artificial intelligence,
theory of computing and complexity, VC dimension, neural networks},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/kuusela-ocone-sontag-as-published-SIAM04.pdf},
ABSTRACT = { This paper takes a computational learning theory
approach to a problem of linear systems identification. It is assumed
that input signals have only a finite number k of frequency
components, and systems to be identified have dimension no greater
than n. The main result establishes that the sample complexity needed
for identification scales polynomially with n and logarithmically
with k. },
DOI = {http://dx.doi.org/10.1137/S0363012901384302}
}
@ARTICLE{MalisoffRiffordSontag04,
AUTHOR = {M. Malisoff and L. Rifford and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Global Asymptotic Controllability Implies Input-to-State
Stabilization},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {2221--2238},
VOLUME = {42},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability, control-Lyapunov functions,
nonlinear control, feedback stabilization},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/malisoff-rifford-sontag-SIAM04.pdf},
ABSTRACT = { The main problem addressed in this paper is the design
of feedbacks for globally asymptotically controllable (GAC) control
affine systems that render the closed loop systems input to state
stable with respect to actuator errors. Extensions for fully
nonlinear GAC systems with actuator errors are also discussed. Our
controllers have the property that they tolerate small observation
noise as well. },
DOI = {http://dx.doi.org/10.1137/S0363012903422333}
}
@ARTICLE{sysbio04,
AUTHOR = {E.D. Sontag},
JOURNAL = {IET Systems Biology},
TITLE = {Some new directions in control theory inspired by
systems biology},
YEAR = {2004},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {9-18},
VOLUME = {1},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems, cellular signaling},
PDF = {../../FTPDIR/sysbio_sontag04.pdf},
ABSTRACT = { This paper, addressed primarily to engineers and
mathematicians with an interest in control theory, argues that
entirely new theoretical problems arise naturally when addressing
questions in the field of systems biology. Examples from the author's
recent work are used to illustrate this point. }
}
@ARTICLE{SontagKiyatinKholodenko04,
AUTHOR = {E.D. Sontag and A. Kiyatkin and B.N. Kholodenko},
JOURNAL = {Bioinformatics},
TITLE = {Inferring dynamic architecture of cellular networks
using time series of gene expression, protein and metabolite data},
YEAR = {2004},
OPTMONTH = {},
NOTE = {Supplementary materials are here: http://sontaglab.org/FTPDIR/sontag-kiyatkin-kholodenko-informatics04-supplement.pdf},
NUMBER = {12},
PAGES = {1877--1886},
VOLUME = {20},
ADDRESS = {Oxford, UK},
KEYWORDS = {modular response analysis, systems biology,
reaction networks, reverse engineering, gene and protein networks,
protein networks, gene networks, systems identification},
PUBLISHER = {Oxford University Press},
PDF = {../../FTPDIR/sontag_kiyatkin_kholodenko_informatics04.pdf},
ABSTRACT = { High-throughput technologies have facilitated the
acquisition of large genomics and proteomics data sets. However,
these data provide snapshots of cellular behavior, rather than help
us reveal causal relations. Here, we propose how these technologies
can be utilized to infer the topology and strengths of connections
among genes, proteins, and metabolites by monitoring time-dependent
responses of cellular networks to experimental interventions. We show
that all connections leading to a given network node, e.g., to a
particular gene, can be deduced from responses to perturbations none
of which directly influences that node, e.g., using strains with
knock-outs to other genes. To infer all interactions from stationary
data, each node should be perturbed separately or in combination with
other nodes. Monitoring time series provides richer information and
does not require perturbations to all nodes. },
DOI = {http://dx.doi.org/10.1093/bioinformatics/bth173}
}
@INPROCEEDINGS{04cdc-circadian,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications},
TITLE = {An analysis of a circadian model using the small-gain
approach to monotone systems},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {575--578},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {circadian rhythms, tridiagonal systems,
nonlinear dynamics, systems biology, reaction networks, oscillations,
periodic behavior, monotone systems, delay-differential systems},
PDF = {../../FTPDIR/04cdc-circadian-final.pdf},
ABSTRACT = { We show how certain properties of Goldbeter's original
1995 model for circadian oscillations can be proved mathematically.
We establish global asymptotic stability, and in particular no
oscillations, if the rate of transcription is somewhat smaller than
that assumed by Goldbeter, but, on the other hand, this stability
persists even under arbitrary delays in the feedback loop. We are
mainly interested in illustrating certain mathematical techniques,
including the use of theorems concerning tridiagonal cooperative
systems and the recently developed theory of monotone systems with
inputs and outputs. }
}
@INPROCEEDINGS{04mtns-angeli-leenheer-monotone,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. 16th Int. Symp. Mathematical Theory of Networks and Systems (MTNS 2004), CD-ROM, WP9.1, Katholieke Universiteit Leuven},
TITLE = {A tutorial on monotone systems- with an application to
chemical reaction networks},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems},
PDF = {../../FTPDIR/04mtns-leenheer-angeli-monotone.pdf},
ABSTRACT = { Monotone systems are dynamical systems for which the
flow preserves a partial order. Some applications will be briefly
reviewed in this paper. Much of the appeal of the class of monotone
systems stems from the fact that roughly, most solutions converge to
the set of equilibria. However, this usually requires a stronger
monotonicity property which is not always satisfied or easy to check
in applications. Following work of J.F. Jiang, we show that
monotonicity is enough to conclude global attractivity if there is a
unique equilibrium and if the state space satisfies a particular
condition. The proof given here is self-contained and does not
require the use of any of the results from the theory of monotone
systems. We will illustrate it on a class of chemical reaction
networks with monotone, but otherwise arbitrary, reaction kinetics. }
}
@INPROCEEDINGS{04cdc-angeli-leenheer-monotone,
AUTHOR = {D. Angeli and de Leenheer, P. and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications},
TITLE = {Remarks on monotonicity and convergence in chemical
reaction networks},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {243--248},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems}
}
@INPROCEEDINGS{04cdc-chaves-dinerstein,
AUTHOR = {M. Chaves and E.D. Sontag and R.J. Dinerstein},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications},
TITLE = {Gains and optimal design in signaling pathways},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {596--601},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, dynamical systems}
}
@INPROCEEDINGS{04acc1,
AUTHOR = {B. DasGupta and J.P. Hespanha and E.D. Sontag},
BOOKTITLE = {Proceedings American Control Conf., Boston, June 2004},
TITLE = {Aggregation-based approaches to honey-pot searching with
local sensory information},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {(CD-ROM WeM17.4, IEEE Publications, Piscataway)},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/04acc-dasgupta-hespanha-sontag-aggregation-search.pdf},
ABSTRACT = { We investigate the problem of searching for a hidden
target in a bounded region by an autonomous agent that is only able
to use limited local sensory information. We propose an
aggregation-based approach to solve this problem, in which the
continuous search space is partitioned into a finite collection of
regions on which we define a discrete search problem. A solution to
the original problem is then obtained through a refinement procedure
that lifts the discrete path into a continuous one. The resulting
solution is in general not optimal but one can construct bounds to
gauge the cost penalty incurred. }
}
@INPROCEEDINGS{04acc2,
AUTHOR = {B. DasGupta and J.P. Hespanha and E.D. Sontag},
BOOKTITLE = {Proceedings American Control Conf., Boston, June 2004, CD-ROM, ThA06.1, IEEE Publications, Piscataway},
TITLE = {Computational complexities of honey-pot searching with
local sensory information},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/04acc-dasgupta-hespanha-sontag-computational-search.pdf},
ABSTRACT = { In this paper we investigate the problem of searching
for a hidden target in a bounded region of the plane, by an
autonomous robot which is only able to use limited local sensory
information. We formalize a discrete version of the problem as a
"reward-collecting" path problem and provide efficient approximation
algorithms for various cases. }
}
@INPROCEEDINGS{04cdc-enciso-multi,
AUTHOR = {G.A. Enciso and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications},
TITLE = {A remark on multistability for monotone systems},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {249--254},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {multistability, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems}
}
@INPROCEEDINGS{04cdc-mancilla-wang-representation,
AUTHOR = {J.L. Mancilla-Aguilar and R. Garca and E.D. Sontag and
Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications},
TITLE = {Representation of switched systems by perturbed control
systems},
YEAR = {2004},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3259--3264},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{posta03chemostat,
AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag},
BOOKTITLE = {Positive systems (Rome, 2003)},
PUBLISHER = {Springer},
TITLE = {A feedback perspective for chemostat models with
crowding effects},
YEAR = {2003},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {167--174},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {294},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems}
}
@INCOLLECTION{MR2019317,
AUTHOR = {de Leenheer, P. and D. Angeli and E.D. Sontag},
BOOKTITLE = {Positive systems (Rome, 2003)},
PUBLISHER = {Springer},
TITLE = {Small-gain theorems for predator-prey systems},
YEAR = {2003},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {191--198},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {294},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems}
}
@ARTICLE{monotoneTAC,
AUTHOR = {D. Angeli and E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Monotone control systems},
YEAR = {2003},
OPTMONTH = {},
NOTE = {Errata are here: http://sontaglab.org/FTPDIR/angeli-sontag-monotone-TAC03-typos.txt},
NUMBER = {10},
PAGES = {1684--1698},
VOLUME = {48},
KEYWORDS = {MAPK cascades, systems biology, reaction networks,
nonlinear stability, dynamical systems, monotone systems},
PDF = {../../FTPDIR/angeli-sontag-monotone-TAC03.pdf},
ABSTRACT = { Monotone systems constitute one of the most important
classes of dynamical systems used in mathematical biology modeling.
The objective of this paper is to extend the notion of monotonicity
to systems with inputs and outputs, a necessary first step in trying
to understand interconnections, especially including feedback loops,
built up out of monotone components. Basic definitions and theorems
are provided, as well as an application to the study of a model of
one of the cell's most important subsystems. }
}
@ARTICLE{DiffISS_IJRNC03,
AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang},
JOURNAL = {Internat. J. Robust Nonlinear Control},
TITLE = {Input-to-state stability with respect to inputs and
their derivatives},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {11},
PAGES = {1035--1056},
VOLUME = {13},
KEYWORDS = {input to state stability, ISS, input to state stability,
ISS},
PDF = {../../FTPDIR/diss-ijrac03.pdf},
ABSTRACT = { A new notion of input-to-state stability involving
infinity norms of input derivatives up to a finite order k is
introduced and characterized. An example shows that this notion of
stability is indeed weaker than the usual ISS. Applications to the
study of global asymptotic stability of cascaded nonlinear systems
are discussed. }
}
@ARTICLE{chyba03,
AUTHOR = {M. Chyba and N. E. Leonard and E.D. Sontag},
JOURNAL = {Journal of Dynamical and Control Systems},
TITLE = {Singular trajectories in multi-input time-optimal
problems: Application to controlled mechanical systems},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {103--129},
VOLUME = {9},
ADDRESS = {Hingham, MA, USA},
KEYWORDS = {optimal control},
PUBLISHER = {Kluwer Academic Publishers},
PDF = {../../FTPDIR/chyba_leonard_sontag_jds2003_reprint.pdf},
ABSTRACT = { This paper addresses the time-optimal control problem
for a class of control systems which includes controlled mechanical
systems with possible dissipation terms. The Lie algebras associated
with such mechanical systems enjoy certain special properties. These
properties are explored and are used in conjunction with the
Pontryagin maximum principle to determine the structure of singular
extremals and, in particular, time-optimal trajectories. The theory
is illustrated with an application to a time-optimal problem for a
class of underwater vehicles. },
DOI = {http://dx.doi.org/10.1023/A:1022159318457}
}
@ARTICLE{relaxation-DE-PAMS03,
AUTHOR = {B.P. Ingalls and E.D. Sontag and Y. Wang},
JOURNAL = {Proc. Amer. Math. Soc.},
TITLE = {An infinite-time relaxation theorem for differential
inclusions},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {487--499},
VOLUME = {131},
PDF = {../../FTPDIR/relaxation-di-as-appeared.pdf},
ABSTRACT = { The fundamental relaxation result for Lipschitz
differential inclusions is the Filippov-Wazewski Relaxation Theorem,
which provides approximations of trajectories of a relaxed inclusion
on finite intervals. A complementary result is presented, which
provides approximations on infinite intervals, but does not guarantee
that the approximation and the reference trajectory satisfy the same
initial condition. }
}
@ARTICLE{moreau_sontagPRE03,
AUTHOR = {L. Moreau and E.D. Sontag},
JOURNAL = {Phys. Rev. E (3)},
TITLE = {Balancing at the border of instability},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {020901, 4},
VOLUME = {68},
KEYWORDS = {bifurcations, adaptive control},
PDF = {../../FTPDIR/moreau-sontag-physrevE03.pdf},
ABSTRACT = { Some biological systems operate at the critical point
between stability and instability and this requires a fine-tuning of
parameters. We bring together two examples from the literature that
illustrate this: neural integration in the nervous system and hair
cell oscillations in the auditory system. In both examples the
question arises as to how the required fine-tuning may be achieved
and maintained in a robust and reliable way. We study this question
using tools from nonlinear and adaptive control theory. We illustrate
our approach on a simple model which captures some of the essential
features of neural integration. As a result, we propose a large class
of feedback adaptation rules that may be responsible for the
experimentally observed robustness of neural integration. We mention
extensions of our approach to the case of hair cell oscillations in
the ear. }
}
@ARTICLE{moreau_sontag_arcak03,
AUTHOR = {L. Moreau and E.D. Sontag and M. Arcak},
JOURNAL = {Systems Control Lett.},
TITLE = {Feedback tuning of bifurcations},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {229--239},
VOLUME = {50},
KEYWORDS = {bifurcations, adaptive control},
PDF = {../../FTPDIR/moreau-sontag-arcak-bifurcations.pdf},
ABSTRACT = { This paper studies a feedback regulation problem that
arises in at least two different biological applications. The
feedback regulation problem under consideration may be interpreted as
an adaptive control problem for tuning bifurcation parameters, and it
has not been studied in the control literature. The goal of the paper
is to formulate this problem and to present some preliminary results. }
}
@ARTICLE{pomerening-ferrell,
AUTHOR = {J. R. Pomerening and E.D. Sontag and J. E. Ferrell},
JOURNAL = {Nature Cell Biology},
TITLE = {Building a cell cycle oscillator: hysteresis and
bistability in the activation of Cdc2},
YEAR = {2003},
OPTMONTH = {},
NOTE = {Supplementary materials 2-4 are here: http://sontaglab.org/FTPDIR/pomerening-sontag-ferrell-additional.pdf},
NUMBER = {4},
PAGES = {346--351},
VOLUME = {5},
ADDRESS = {Department of Molecular Pharmacology, Stanford University School of Medicine, Stanford, CA 94305-5174, USA.},
KEYWORDS = {systems biology, reaction networks, oscillations,
nonlinear stability, dynamical systems, monotone systems},
URL = {http://dx.doi.org/10.1038/ncb954},
PDF = {../../FTPDIR/pomerening-sontag-ferrell-naturecell03.pdf},
ABSTRACT = { In the early embryonic cell cycle, Cdc2-cyclin B
functions like an autonomous oscillator, at whose core is a negative
feedback loop: cyclins accumulate and produce active mitotic
Cdc2-cyclin B Cdc2 activates the anaphase-promoting complex (APC);
the APC then promotes cyclin degradation and resets Cdc2 to its
inactive, interphase state. Cdc2 regulation also involves positive
feedback4, with active Cdc2-cyclin B stimulating its activator Cdc25
and inactivating its inhibitors Wee1 and Myt1. Under the correct
circumstances, these positive feedback loops could function as a
bistable trigger for mitosis, and oscillators with bistable triggers
may be particularly relevant to biological applications such as cell
cycle regulation. This paper examined whether Cdc2 activation is
bistable, confirming that the response of Cdc2 to non-degradable
cyclin B is temporally abrupt and switchlike, as would be expected if
Cdc2 activation were bistable. It is also shown that Cdc2 activation
exhibits hysteresis, a property of bistable systems with particular
relevance to biochemical oscillators. These findings help establish
the basic systems-level logic of the mitotic oscillator. },
DOI = {10.1038/ncb954}
}
@ARTICLE{CICS_TAC03,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {A remark on the converging-input converging-state
property},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {313--314},
VOLUME = {48},
PDF = {../../FTPDIR/cics-TAC03-as-appeared.pdf},
ABSTRACT = { Suppose that an equilibrium is asymptotically stable
when external inputs vanish. Then, every bounded trajectory which
corresponds to a control which approaches zero and which lies in the
domain of attraction of the unforced system, must also converge to
the equilibrium. This "well-known" but hard-to-cite fact is proved
and slightly generalized here. }
}
@ARTICLE{imp03,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Adaptation and regulation with signal detection implies
internal model},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {119--126},
VOLUME = {50},
KEYWORDS = {biological adaptation, internal model principle},
PDF = {../../FTPDIR/imp-scl03.pdf},
ABSTRACT = { This note provides a simple result showing, under
suitable technical assumptions, that if a system S adapts to a class
of external signals U, then S must necessarily contain a subsystem
which is capable of generating all the signals in U. It is not
assumed that regulation is robust, nor is there a prior requirement
for the system to be partitioned into separate plant and controller
components. Instead, a "signal detection" capability is imposed.
These weaker assumptions make the result better applicable to
cellular phenomena such as the adaptation of E-coli chemotactic
tumbling rate to constant concentrations. }
}
@ARTICLE{sontag_krichman_integrable_perturb_TAC03,
AUTHOR = {E.D. Sontag and M. Krichman},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {An example of a GAS system which can be destabilized by
an integrable perturbation},
YEAR = {2003},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1046--1049},
VOLUME = {48},
KEYWORDS = {nonlinear stability},
PDF = {../../FTPDIR/L1-perturb-GAS.pdf},
ABSTRACT = { A construction is given of a globally asymptotically
stable time-invariant system which can be destabilized by some
integrable perturbation. Besides its intrinsic interest, this serves
to provide counterexamples to an open question regarding Lyapunov
functions. }
}
@INPROCEEDINGS{angeli-03cdc-multistability,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003},
TITLE = {A note on multistability and monotone I/O systems},
YEAR = {2003},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {67--72},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems biology, reaction networks, nonlinear stability,
dynamical systems, monotone systems}
}
@INPROCEEDINGS{malisoff-rifford-03cdc,
AUTHOR = {M. Malisoff and L. Rifford and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003},
TITLE = {Remarks on input to state stabilization},
YEAR = {2003},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1053--1058},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {nonlinear control, feedback stabilization},
PDF = {../../FTPDIR/malisoff_rifford_sontag_2003cdc.pdf}
}
@INPROCEEDINGS{moreau-arcak-03cdc,
AUTHOR = {L. Moreau and E.D. Sontag and M. Arcak},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Maui, Dec. 2003, IEEE Publications, 2003},
TITLE = {How feedback can tune a bifurcation parameter towards
its unknown critical bifurcation value},
YEAR = {2003},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2401--2406},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@ARTICLE{arcak_angeli_sontag_cascades_SICOPT02,
AUTHOR = {M. Arcak and D. Angeli and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {A unifying integral ISS framework for stability of
nonlinear cascades},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1888--1904},
VOLUME = {40},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/iiss-cascades.pdf},
ABSTRACT = { We analyze nonlinear cascades in which the driven
subsystem is integral ISS, and characterize the admissible integral
ISS gains for stability. This characterization makes use of the
convergence speed of the driving subsystem, and allows a larger class
of gain functions when the convergence is faster. We show that our
integral ISS gain characterization unifies different approaches in
the literature which restrict the nonlinear growth of the driven
subsystem and the convergence speed of the driving subsystem. },
DOI = {http://dx.doi.org/10.1137/S0363012901387987}
}
@ARTICLE{chem-obs-journal,
AUTHOR = {M. Chaves and E.D. Sontag},
JOURNAL = {European J. Control},
TITLE = {State-Estimators for chemical reaction networks of
Feinberg-Horn-Jackson zero deficiency type},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {343--359},
VOLUME = {8},
KEYWORDS = {observability, zero-deficiency networks,
systems biology, reaction networks, observers, nonlinear stability,
dynamical systems},
PDF = {../../FTPDIR/chem-observers.pdf},
ABSTRACT = { This paper provides a necessary and sufficient
condition for detectability, and an explicit construction of
observers when this condition is satisfied, for chemical reaction
networks of the Feinberg-Horn-Jackson zero deficiency type. }
}
@ARTICLE{kholodenkoPNAS02,
AUTHOR = {B.N. Kholodenko and A. Kiyatkin and F.J. Bruggeman and
E.D. Sontag and H.V. Westerhoff and J. Hoek},
JOURNAL = {Proceedings of the National Academy of Sciences USA},
TITLE = {Untangling the wires: a novel strategy to trace
functional interactions in signaling and gene networks},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {12841--12846},
VOLUME = {99},
KEYWORDS = {modular response analysis, MAPK cascades,
systems biology, reaction networks, reverse engineering,
gene and protein networks, protein networks, gene networks,
systems identification},
PDF = {../../FTPDIR/unravel_pnas02_including_supporting.pdf},
ABSTRACT = { Emerging technologies have enabled the acquisition of
large genomics and proteomics data sets. This paper proposes a novel
quantitative method for determining functional interactions in
cellular signaling and gene networks. It can be used to explore cell
systems at a mechanistic level, or applied within a modular
framework, which dramatically decreases the number of variables to be
assayed. The topology and strength of network connections are
retrieved from experimentally measured network responses to
successive perturbations of all modules. In addition, the method can
reveal functional interactions even when the components of the system
are not all known, in which case some connections retrieved by the
analysis will not be direct but correspond to the interaction routes
through unidentified elements. The method is tested and illustrated
using computer-generated responses of a modeled MAPK cascade and gene
network. }
}
@ARTICLE{IOSS_discontinuous_IJC02,
AUTHOR = {M. Krichman and E.D. Sontag},
JOURNAL = {Internat. J. Control},
TITLE = {Characterizations of detectability notions in terms of
discontinuous dissipation functions},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {12},
PAGES = {882--900},
VOLUME = {75},
KEYWORDS = {input to state stability, detectability,
input to output stability, detectability},
PDF = {../../FTPDIR/ioss-nonsmooth.pdf},
ABSTRACT = { We consider a new Lyapunov-type characterization of
detectability for nonlinear systems without controls, in terms of
lower-semicontinuous (not necessarily smooth, or even continuous)
dissipation functions, and prove its equivalence to the GASMO (global
asymptotic stability modulo outputs) and UOSS (uniform
output-to-state stability) properties studied in previous work. The
result is then extended to provide a construction of a discontinuous
dissipation function characterization of the IOSS (input-to-state
stability) property for systems with controls. This paper complements
a recent result on smooth Lyapunov characterizations of IOSS. The
utility of non-smooth Lyapunov characterizations is illustrated by
application to a well-known transistor network example. }
}
@ARTICLE{liberzon_morse_sontag_minphase_TAC02,
AUTHOR = {D. Liberzon and A. S. Morse and E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Output-input stability and minimum-phase nonlinear
systems},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {422--436},
VOLUME = {47},
KEYWORDS = {input to state stability, detectability,
minimum-phase systems, ISS, nonlinear control, minimum phase,
adaptive control},
PDF = {../../FTPDIR/minphase.pdf},
ABSTRACT = { This paper introduces and studies a new definition of
the minimum-phase property for general smooth nonlinear control
systems. The definition does not rely on a particular choice of
coordinates in which the system takes a normal form or on the
computation of zero dynamics. In the spirit of the ``input-to-state
stability'' philosophy, it requires the state and the input of the
system to be bounded by a suitable function of the output and
derivatives of the output, modulo a decaying term depending on
initial conditions. The class of minimum-phase systems thus defined
includes all affine systems in global normal form whose internal
dynamics are input-to-state stable and also all left-invertible
linear systems whose transmission zeros have negative real parts. As
an application, we explain how the new concept enables one to develop
a natural extension to nonlinear systems of a basic result from
linear adaptive control. }
}
@ARTICLE{liberzon_sontag_wang_universalISS_SCL02,
AUTHOR = {D. Liberzon and E.D. Sontag and Y. Wang},
JOURNAL = {Systems Control Lett.},
TITLE = {Universal construction of feedback laws achieving ISS
and integral-ISS disturbance attenuation},
YEAR = {2002},
OPTMONTH = {},
NOTE = {Errata here: http://sontaglab.org/FTPDIR/iiss-clf-errata.pdf},
NUMBER = {2},
PAGES = {111--127},
VOLUME = {46},
KEYWORDS = {input to state stability,
integral input to state stability, ISS, iISS, nonlinear control,
feedback stabilization},
PDF = {../../FTPDIR/iISS-CLFs.pdf},
ABSTRACT = { We study nonlinear systems with both control and
disturbance inputs. The main problem addressed in the paper is design
of state feedback control laws that render the closed-loop system
integral-input-to-state stable (iISS) with respect to the
disturbances. We introduce an appropriate concept of control Lyapunov
function (iISS-CLF), whose existence leads to an explicit
construction of such a control law. The same method applies to the
problem of input-to-state stabilization. Converse results and
techniques for generating iISS-CLFs are also discussed. }
}
@ARTICLE{cauchySCL02,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Asymptotic amplitudes and Cauchy gains: A small-gain
principle and an application to inhibitory biological feedback},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {167--179},
VOLUME = {47},
KEYWORDS = {MAPK cascades, cyclic feedback systems, small-gain},
PDF = {../../FTPDIR/cauchy-gains-scl-as-published.pdf},
ABSTRACT = { The notions of asymptotic amplitude for signals, and
Cauchy gain for input/output systems, and an associated small-gain
principle, are introduced. These concepts allow the consideration of
systems with multiple, and possibly feedback-dependent, steady
states. A Lyapunov-like characterization allows the computation of
gains for state-space systems, and the formulation of sufficient
conditions insuring the lack of oscillations and chaotic behaviors in
a wide variety of cascades and feedback loops. An application in
biology (MAPK signaling) is worked out in detail. }
}
@ARTICLE{MR1893535,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Correction to: ``Structure and stability of certain
chemical networks and applications to the kinetic proofreading model
of T-cell receptor signal transduction'' [IEEE Trans. Automat.
Control 46 (2001), no. 7, 1028--1047; MR1842137 (2002e:92006)]},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {705},
VOLUME = {47},
KEYWORDS = {zero-deficiency networks, systems biology,
reaction networks, nonlinear stability, dynamical systems},
PDF = {../../FTPDIR/chem-errata.pdf},
ABSTRACT = { errata for Structure and stability of certain chemical
networks and applications to the kinetic proofreading model of T-cell
receptor signal transduction }
}
@ARTICLE{ident_experiments02,
AUTHOR = {E.D. Sontag},
JOURNAL = {J. Nonlinear Sci.},
TITLE = {For differential equations with r parameters, 2r+1
experiments are enough for identification},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {553--583},
VOLUME = {12},
KEYWORDS = {identifiability, observability, systems biology,
reaction networks, parameter identification, real-analytic functions},
PDF = {../../FTPDIR/ident-experiments.pdf},
ABSTRACT = { Given a set of differential equations whose description
involves unknown parameters, such as reaction constants in chemical
kinetics, and supposing that one may at any time measure the values
of some of the variables and possibly apply external inputs to help
excite the system, how many experiments are sufficient in order to
obtain all the information that is potentially available about the
parameters? This paper shows that the best possible answer (assuming
exact measurements and real analiticity) is 2r+1 experiments, where r
is the number of parameters. }
}
@ARTICLE{sontag_ingalls_small_gain_JFI02,
AUTHOR = {E.D. Sontag and B.P. Ingalls},
JOURNAL = {J. Franklin Inst.},
TITLE = {A small-gain theorem with applications to input/output
systems, incremental stability, detectability, and interconnections},
YEAR = {2002},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {211--229},
VOLUME = {339},
KEYWORDS = {input to state stability, ISS, Small-Gain Theorem,
small gain},
PDF = {../../FTPDIR/small-gain-as-published.pdf},
ABSTRACT = { A general ISS-type small-gain result is presented. It
specializes to a small-gain theorem for ISS operators, and it also
recovers the classical statement for ISS systems in state-space form.
In addition, we highlight applications to incrementally stable
systems, detectable systems, and to interconnections of stable
systems. }
}
@INPROCEEDINGS{02cdc-monotone,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications},
TITLE = {A remark on monotone control systems},
YEAR = {2002},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1876--1881},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{02cdc-liberzon-hespanha,
AUTHOR = {J.P. Hespanha and D. Liberzon and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications},
TITLE = {Nonlinear observability and an invariance principle for
switched systems},
YEAR = {2002},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4300--4305},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {observability},
PDF = {../../FTPDIR/02cdc-liberzon-hespanha-as-sent.pdf}
}
@INPROCEEDINGS{02mtns-relaxation,
AUTHOR = {B.P. Ingalls and E.D. Sontag and Y. Wang},
BOOKTITLE = {Mathematical Theory of Networks and Systems, Electronic Proceedings of MTNS-2002 Symposium held at the University of Notre Dame, August 2002},
TITLE = {A relaxation theorem for differential inclusions with
applications to stability properties},
YEAR = {2002},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {D. Gilliam and J. Rosenthal},
OPTMONTH = {},
NOTE = {(12 pages)},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/02mtns-ingalls-sontag-wang.pdf},
ABSTRACT = { The fundamental Filippov--Wazwski Relaxation Theorem
states that the solution set of an initial value problem for a
locally Lipschitz inclusion is dense in the solution set of the same
initial value problem for the corresponding relaxation inclusion on
compact intervals. In a recent paper of ours, a complementary result
was provided for inclusions with finite dimensional state spaces
which says that the approximation can be carried out over non-compact
or infinite intervals provided one does not insist on the same
initial values. This note extends the infinite-time relaxation
theorem to the inclusions whose state spaces are Banach spaces. To
illustrate the motivations for studying such approximation results,
we briefly discuss a quick application of the result to output
stability and uniform output stability properties. }
}
@INPROCEEDINGS{02cdc-mes,
AUTHOR = {B.P. Ingalls and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications},
TITLE = {Measurement to error stability: a notion of partial
detectability for nonlinear systems},
YEAR = {2002},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3946--3951},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability},
PDF = {../../FTPDIR/02cdc-ingalls-sontag-wang-published.pdf},
ABSTRACT = { For systems whose output is to be kept small (thought
of as an error output), the notion of input to output stability (IOS)
arises. Alternatively, when considering a system whose output is
meant to provide information about the state (i.e. a measurement
output), one arrives at the detectability notion of output to state
stability (OSS). Combining these concepts, one may consider a system
with two types of outputs, an error and a measurement. This leads
naturally to a notion of partial detectability which we call
measurement to error stability (MES). This property characterizes
systems in which the error signal is detectable through the
measurement signal. This paper provides a partial Lyapunov
characterization of the MES property. A closely related property of
stability in three measures (SIT) is introduced, which characterizes
systems for which the error decays whenever it dominates the
measurement. The SIT property is shown to imply MES, and the two are
shown to be equivalent under an additional boundedness assumption. A
nonsmooth Lyapunov characterization of the SIT property is provided,
which yields the partial characterization of MES. The analysis is
carried out on systems described by differential inclusions --
implicitly incorporating a disturbance input with compact value-set. }
}
@INPROCEEDINGS{02cdc-cauchy-gains,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications},
TITLE = {Asymptotic amplitudes, Cauchy gains, an associated
small-gain principle, and an application to inhibitory biological
feedback},
YEAR = {2002},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4318--4323},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {cyclic feedback systems, small-gain}
}
@INBOOK{AntoulasSontagYamamoto2001,
PUBLISHER = {John Wiley & Sons, Inc.},
TITLE = {Controllability and Observability},
YEAR = {2001},
AUTHOR = {A. C. Antoulas and E. D. Sontag and Y. Yamamoto},
ALTCHAPTER = {},
ALTEDITOR = {},
PAGES = {264-281},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
BOOKTITLE = {Wiley Encyclopedia of Electrical and Electronics Engineering},
KEYWORDS = {reachability, controllability, observability,
Lie algebra accessibility},
URL = {http://dx.doi.org/10.1002/047134608X.W1006},
PDF = {../../FTPDIR/antoulas_sontag_yamamoto_controllability_observability_wiley_encyclopedia_electrical_electronics_engineering_2001.pdf},
DOI = {10.1002/047134608X.W1006}
}
@INCOLLECTION{MR1806191,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Nonlinear control in the year 2000, Vol. 2 (Paris)},
PUBLISHER = {Springer},
TITLE = {The ISS philosophy as a unifying framework for
stability-like behavior},
YEAR = {2001},
ADDRESS = {London},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {443--467},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {259},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
input to output stability},
PDF = {../../FTPDIR/00paris.pdf},
ABSTRACT = { (This is an expository paper prepared for a plenary
talk given at the Second Nonlinear Control Network Workshop, Paris,
June 9, 2000.) The input to state stability (ISS) paradigm is
motivated as a generalization of classical linear systems concepts
under coordinate changes. A summary is provided of the main
theoretical results concerning ISS and related notions of
input/output stability and detectability. A bibliography is also
included, listing extensions, applications, and other current work. }
}
@ARTICLE{TCShybrid01,
AUTHOR = {B. DasGupta and E.D. Sontag},
JOURNAL = {Theor. Comput. Sci.},
TITLE = {A polynomial-time algorithm for checking equivalence
under certain semiring congruences motivated by the state-space
isomorphism problem for hybrid systems},
YEAR = {2001},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1-2},
PAGES = {161--189},
VOLUME = {262},
ADDRESS = {Essex, UK},
KEYWORDS = {hybrid systems, computational complexity},
PUBLISHER = {Elsevier Science Publishers Ltd.},
PDF = {../../FTPDIR/pl-decide.pdf},
ABSTRACT = { The area of hybrid systems concerns issues of modeling,
computation, and control for systems which combine discrete and
continuous components. The subclass of piecewise linear (PL) systems
provides one systematic approach to discrete-time hybrid systems,
naturally blending switching mechanisms with classical linear
components. PL systems model arbitrary interconnections of finite
automata and linear systems. Tools from automata theory, logic, and
related areas of computer science and finite mathematics are used in
the study of PL systems, in conjunction with linear algebra
techniques, all in the context of a "PL algebra" formalism. PL
systems are of interest as controllers as well as identification
models. Basic questions for any class of systems are those of
equivalence, and, in particular, if state spaces are equivalent under
a change of variables. This paper studies this state-space
equivalence problem for PL systems. The problem was known to be
decidable, but its computational complexity was potentially
exponential; here it is shown to be solvable in polynomial-time. },
DOI = {http://dx.doi.org/10.1016/S0304-3975(00)00188-2}
}
@ARTICLE{desch_logemann_ryan_sontag_meagre_NA01,
AUTHOR = {W. Desch and H. Logemann and E. P. Ryan and E.D. Sontag},
JOURNAL = {Nonlinear Anal.},
TITLE = {Meagre functions and asymptotic behaviour of dynamical
systems},
YEAR = {2001},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {8, Ser. A: Theory Methods},
PAGES = {1087--1109},
VOLUME = {44},
ADDRESS = {Oxford, UK, UK},
KEYWORDS = {invariance principle},
PUBLISHER = {Elsevier Science Ltd.},
PDF = {../../FTPDIR/ryan-logeman.pdf},
ABSTRACT = { A measurable function x from a subset J of R into a
metric space X is said to be C-meagre if C is non-empty subset of X
and, for every closed subset K of X disjoint from C, the preimage of
K under x has finite Lebesgue measure. This concept of meagreness,
applied to trajectories, is shown to provide a unifying framework
which facilitates a variety of characterizations, extensions or
generalizations of diverse facts pertaining to asymptotic behaviour
of dynamical systems. },
DOI = {http://dx.doi.org/10.1016/S0362-546X(99)00323-5}
}
@ARTICLE{krichman_sontag_wang_IOSS_01,
AUTHOR = {M. Krichman and E.D. Sontag and Y. Wang},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Input-output-to-state stability},
YEAR = {2001},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1874--1928},
VOLUME = {39},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/ioss_input_output_to_state_krichman_sontag_wang_reprint_siam2001.pdf},
ABSTRACT = { This work explores Lyapunov characterizations of the
input-output-to-state stability (IOSS) property for nonlinear
systems. The notion of IOSS is a natural generalization of the
standard zero-detectability property used in the linear case. The
main contribution of this work is to establish a complete equivalence
between the input-output-to-state stability property and the
existence of a certain type of smooth Lyapunov function. As
corollaries, one shows the existence of "norm-estimators", and
obtains characterizations of nonlinear detectability in terms of
relative stability and of finite-energy estimates. },
DOI = {http://dx.doi.org/10.1137/S0363012999365352}
}
@ARTICLE{Tcell01,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Structure and stability of certain chemical networks and
applications to the kinetic proofreading model of T-cell receptor
signal transduction},
YEAR = {2001},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {7},
PAGES = {1028--1047},
VOLUME = {46},
KEYWORDS = {zero-deficiency networks, systems biology,
reaction networks, nonlinear stability, dynamical systems,
kinetic proofreading, T cells, immunology},
PDF = {../../FTPDIR/chem.pdf},
ABSTRACT = { This paper deals with the theory of structure,
stability, robustness, and stabilization for an appealing class of
nonlinear systems which arises in the analysis of chemical networks.
The results given here extend, but are also heavily based upon,
certain previous work by Feinberg, Horn, and Jackson, of which a
self-contained and streamlined exposition is included. The
theoretical conclusions are illustrated through an application to the
kinetic proofreading model proposed by McKeithan for T-cell receptor
signal transduction. }
}
@INPROCEEDINGS{01nolcos-diss,
AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001},
TITLE = {A note on input-to-state stability with input
derivatives},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {720--725},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS}
}
@INPROCEEDINGS{01cdc-arcak,
AUTHOR = {M. Arcak and D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001},
TITLE = {Stabilization of cascades using integral input-to-state
stability},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3814--3819},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {nonlinear control, feedback stabilization,
input to state stability}
}
@INPROCEEDINGS{01nolcos-chaves,
AUTHOR = {M. Chaves and E.D. Sontag},
BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001},
TITLE = {An alternative observer for zero deficiency chemical
networks},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {575--578},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {observability, observers, zero-deficiency networks,
systems biology, reaction networks, nonlinear stability,
dynamical systems}
}
@INPROCEEDINGS{01ecc-chaves,
AUTHOR = {M. Chaves and E.D. Sontag},
BOOKTITLE = {Proc. 2001 European Control Conf., Sep. 2001},
TITLE = {Observers for certain chemical reaction networks},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3715--3720},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {zero-deficiency networks, systems biology,
reaction networks, nonlinear stability, dynamical systems,
observability, observers}
}
@INPROCEEDINGS{01cdc-chyba,
AUTHOR = {M. Chyba and N.E. Leonard and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001,IEEE Publications, 2001},
TITLE = {Optimality for underwater vehicles},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4204--4209},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {optimal control},
PDF = {../../FTPDIR/chyba_leonard_sontag_cdc2001.pdf}
}
@INPROCEEDINGS{01cdc-angeli-ingalls-wang,
AUTHOR = {B.P. Ingalls and D. Angeli and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001},
TITLE = {Asymptotic characterizations of IOSS},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {881--886},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {nonlinear control, feedback stabilization,
input to state stability}
}
@INPROCEEDINGS{01ifac-kuusela,
AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag},
BOOKTITLE = {IFAC Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP2001, Cernobbio-Como, Italy, 29-31 August, 2001},
TITLE = {Remarks on the sample complexity for linear control
systems identification},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {431--436},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{01nolcos-minphase,
AUTHOR = {D. Liberzon and A.S. Morse and E.D. Sontag},
BOOKTITLE = {Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001},
TITLE = {Output-input stability: a new variant of the
minimum-phase property for nonlinear systems},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {743--748},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability}
}
@INPROCEEDINGS{01acc-ingalls,
AUTHOR = {E.D. Sontag and B.P. Ingalls and Y. Wang},
BOOKTITLE = {Proc. American Control Conf., Arlington, June 2001},
TITLE = {Generalizations of asymptotic gain characterizations of
ISS to input-to-output stability},
YEAR = {2001},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2279--2284},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS}
}
@INCOLLECTION{MR1870247,
AUTHOR = {L. Grne and E.D. Sontag and F.R. Wirth},
BOOKTITLE = {International Conference on Differential Equations, Vol. 1, 2 (Berlin, 1999)},
PUBLISHER = {World Sci. Publishing},
TITLE = {On equivalence of exponential and asymptotic stability
under changes of variables},
YEAR = {2000},
ADDRESS = {River Edge, NJ},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {850--852},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability}
}
@ARTICLE{angeli_sontag_wang_iISS_TAC00,
AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {A characterization of integral input-to-state stability},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1082--1097},
VOLUME = {45},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS},
PDF = {../../FTPDIR/iiss-asw.pdf},
ABSTRACT = { Just as input to state stability (ISS) generalizes the
idea of finite gains with respect to supremum norms, the new notion
of integral input to state stability (IISS) generalizes the concept
of finite gain when using an integral norm on inputs. In this paper,
we obtain a necessary and sufficient characterization of the IISS
property, expressed in terms of dissipation inequalities. }
}
@ARTICLE{angeli_sontag_wang_further_equiv_DYNA00,
AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang},
JOURNAL = {Dynamics and Control},
TITLE = {Further equivalences and semiglobal versions of integral
input to state stability},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {127--149},
VOLUME = {10},
ADDRESS = {Hingham, MA, USA},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS},
PUBLISHER = {Kluwer Academic Publishers},
PDF = {../../FTPDIR/iiss_new_integral_iss_angeli_sontag_wang_reprint_dynamics_and_control2000.pdf},
ABSTRACT = { This paper continues the study of the integral
input-to-state stability (IISS) property. It is shown that the IISS
property is equivalent to one which arises from the consideration of
mixed norms on states and inputs, as well as to the superposition of
a ``bounded energy bounded state'' requirement and the global
asymptotic stability of the unforced system. A semiglobal version of
IISS is shown to imply the global version, though a counterexample
shows that the analogous fact fails for input to state stability
(ISS). The results in this note complete the basic theoretical
picture regarding IISS and ISS. },
DOI = {http://dx.doi.org/10.1023/A:1008356223747}
}
@ARTICLE{bao_lin_sontag_dt_saturation_automatica00,
AUTHOR = {X. Bao and Z. Lin and E.D. Sontag},
JOURNAL = {Automatica},
TITLE = {Finite gain stabilization of discrete-time linear
systems subject to actuator saturation},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {269--277},
VOLUME = {36},
KEYWORDS = {discrete-time, saturation, input-to-state stability,
stabilization, ISS, bounded inputs},
PDF = {../../FTPDIR/sat-dt-iss.pdf},
ABSTRACT = { It is shown that, for neutrally stable discrete-time
linear systems subject to actuator saturation, finite gain lp
stabilization can be achieved by linear output feedback, for all p>1.
An explicit construction of the corresponding feedback laws is given.
The feedback laws constructed also result in a closed-loop system
that is globally asymptotically stable, and in an input-to-state
estimate. }
}
@ARTICLE{maass_sontag_filters_NC00,
AUTHOR = {W. Maass and E.D. Sontag},
JOURNAL = {Neural Computation},
TITLE = {Neural Systems as Nonlinear Filters},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {8},
PAGES = {1743--1772},
VOLUME = {12},
ADDRESS = {Cambridge, MA, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, Volterra series},
PUBLISHER = {MIT Press},
PDF = {../../FTPDIR/maass_sontag_neural_systems_as_filters_neural_computation2000.pdf},
ABSTRACT = { We analyze computations on temporal patterns and
spatio-temporal patterns in formal network models whose temporal
dynamics arises from empirically established quantitative models for
short term dynamics at biological synapses. We give a complete
characterization of all linear and nonlinear filters that can be
approximated by such dynamic network models: it is the class of all
filters that can be approximated by Volterra series. This
characterization is shown to be rather stable with regard to changes
in the model. For example it is shown that synaptic facilitation and
one layer of neurons suffices for approximating arbitrary filters
from this class. Our results provide a new complexity hierarchy for
all filters that are approximable by Volterra series, which appears
to be closer related to the actual cost of implementing such filters
in neural hardware than preceding complexity measures. Our results
also provide a new parameterization for approximations to such
filters in terms of parameters that are arguable related to those
that are tunable in biological neural systems. },
DOI = {http://dx.doi.org/10.1162/089976600300015123}
}
@ARTICLE{MR1828059,
AUTHOR = {M. Malisoff and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Universal formulas for feedback stabilization with
respect to Minkowski balls},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {247--260},
VOLUME = {40},
KEYWORDS = {nonlinear control, feedback stabilization, saturation,
control-Lyapunov functions, bounded inputs},
PDF = {../../FTPDIR/minkowski.pdf},
ABSTRACT = { This note provides explicit algebraic stabilizing
formulas for clf's when controls are restricted to certain Minkowski
balls in Euclidean space. Feedbacks of this kind are known to exist
by a theorem of Artstein, but the proof of Artstein's theorem is
nonconstructive. The formulas are obtained from a general feedback
stabilization technique and are used to construct approximation
solutions to some stabilization problems. }
}
@ARTICLE{rosier_sontag_gap_SCL00,
AUTHOR = {L. Rosier and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Remarks regarding the gap between continuous, Lipschitz,
and differentiable storage functions for dissipation inequalities
appearing in H infinity control},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {237--249},
VOLUME = {41},
KEYWORDS = {viscosity solutions, H-infinity control},
PDF = {../../FTPDIR/hoo.pdf},
ABSTRACT = { This paper deals with the regularity of solutions of
the Hamilton-Jacobi Inequality which arises in H-infinity control. It
shows by explicit counterexamples that there are gaps between
existence of continuous and locally Lipschitz (positive definite and
proper) solutions, and between Lipschitz and continuously
differentiable ones. On the other hand, it is shown that it is always
possible to smooth-out solutions, provided that an infinitesimal
increase in gain is allowed. }
}
@ARTICLE{sontag_wang_Lyapunov_IOS_SICOPT00,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Lyapunov characterizations of input to output stability},
YEAR = {2000},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {226--249},
VOLUME = {39},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/lios_lyapunov_characterizations_iostability_wang_sontag_reprint_siam2000.pdf},
ABSTRACT = { This paper presents necessary and sufficient
characterizations of several notions of input to output stability.
Similar Lyapunov characterizations have been found to play a key role
in the analysis of the input to state stability property, and the
results given here extend their validity to the case when the output,
but not necessarily the entire internal state, is being regulated. },
DOI = {http://dx.doi.org/10.1137/S0363012999350213}
}
@INPROCEEDINGS{chyba-IFAC,
AUTHOR = {M. Chyba and N.E. Leonard and E.D. Sontag},
BOOKTITLE = {Lagrangian and Hamiltonian Methods for Nonlinear Control},
TITLE = {Time-optimal control for underwater vehicles},
YEAR = {2000},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {N.E. Leonard and R. Ortega},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {117--122},
PUBLISHER = {Pergamon Press, Oxford},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/chyba_leonard_sontag_IFAC2000.ps}
}
@INPROCEEDINGS{00cdc-minphase,
AUTHOR = {D. Liberzon and A.S. Morse and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Sydney, Dec. 2000, IEEE Publications, 2000},
TITLE = {A new definition of the minimum-phase property for
nonlinear systems, with an application to adaptive control},
YEAR = {2000},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2106--2111},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{00nips,
AUTHOR = {T. Natschlger and W. Maass and E.D. Sontag and A. Zador},
BOOKTITLE = {Advances in Neural Information Processing Systems 13 (NIPS2000)},
TITLE = {Processing of time series by neural circuits with
biologically realistic synaptic dynamics},
YEAR = {2000},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {Todd K. Leen and T. G. Dietterich and V. Tresp},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-13, Denver, 2000, https://papers.nips.cc/paper_files/paper/2000},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {145--151},
PUBLISHER = {MIT Press, Cambridge},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks, Volterra series},
PDF = {../../FTPDIR/2000nips.pdf},
ABSTRACT = { Experimental data show that biological synapses are
dynamic, i.e., their weight changes on a short time scale by several
hundred percent in dependence of the past input to the synapse. In
this article we explore the consequences that this synaptic dynamics
entails for the computational power of feedforward neural networks.
It turns out that even with just a single hidden layer such networks
can approximate a surprisingly large large class of nonlinear
filters: all filters that can be characterized by Volterra series.
This result is robust with regard to various changes in the model for
synaptic dynamics. Furthermore we show that simple gradient descent
suffices to approximate a given quadratic filter by a rather small
neural system with dynamic synapses. }
}
@BOOK{openprob,
PUBLISHER = {Springer Verlag},
TITLE = {Open Problems in Mathematical Systems and Control Theory
(edited book)},
YEAR = {1999},
AUTHOR = {V.D. Blondel and E.D Sontag and M. Vidyasagar and
J.C. Willems},
ALTEDITOR = {},
OPTADDRESS = {},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{MR1727964,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Open problems in mathematical systems and control theory},
PUBLISHER = {Springer},
TITLE = {Control-Lyapunov functions},
YEAR = {1999},
ADDRESS = {London},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {211--216},
SERIES = {Comm. Control Engrg. Ser.},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/1999_control_lyapunov_functions_open_problems_book.pdf},
ABSTRACT = {The main objective of control is to modify the behavior
of a dynamical system, typically with the purpose of regulating
certain variables or of tracking desired signals. Often, either
stability of the closed-loop system is an explicit requirement, or
else the problem can be recast in a form that involves stabilization
(e.g., of an error signal). For linear systems, the associated
problems can now be treated fairly satisfactorily, but in the
nonlinear case the area is still far from being settled. Both of the
late 1980s reports [9] and [18], with dealt with challenges and
future directions for research in control theory, identified the
problem of stabilization of finite-dimensional deterministic systems
as one of the most important open problems in nonlinear control. We
discuss some questions in this area.}
}
@INCOLLECTION{MR1684843,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Dynamical systems, control, coding, computer vision (MTNS Padova, 1998)},
PUBLISHER = {Birkhuser},
TITLE = {Nonlinear feedback stabilization revisited},
YEAR = {1999},
ADDRESS = {Basel},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {The materials in here are a subset of the full version Stability and stabilization: discontinuities and the effect of disturbances},
OPTNUMBER = {},
PAGES = {223--262},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {25},
PDF = {../../FTPDIR/1999_mtns_feedback_stabilization_revisited.pdf}
}
@INCOLLECTION{montreal98,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Nonlinear analysis, differential equations and control (Montreal, QC, 1998)},
PUBLISHER = {Kluwer Acad. Publ.},
TITLE = {Stability and stabilization: discontinuities and the
effect of disturbances},
YEAR = {1999},
ADDRESS = {Dordrecht},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {551--598},
SERIES = {NATO Sci. Ser. C Math. Phys. Sci.},
OPTTYPE = {},
VOLUME = {528},
KEYWORDS = {feedback stabilization, nonlinear control,
input to state stability},
PDF = {../../FTPDIR/stab-survey98.pdf},
ABSTRACT = { In this expository paper, we deal with several
questions related to stability and stabilization of nonlinear
finite-dimensional continuous-time systems. We review the basic
problem of feedback stabilization, placing an emphasis upon
relatively new areas of research which concern stability with respect
to "noise" (such as errors introduced by actuators or sensors). The
table of contents is as follows: Review of Stability and Asymptotic
Controllability, The Problem of Stabilization, Obstructions to
Continuous Stabilization, Control-Lyapunov Functions and Artstein's
Theorem, Discontinuous Feedback, Nonsmooth CLF's, Insensitivity to
Small Measurement and Actuator Errors, Effect of Large Disturbances:
Input-to-State Stability, Comments on Notions Related to ISS. }
}
@ARTICLE{MR1733874,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {Internat. J. Control},
TITLE = {Continuous control-Lyapunov functions for asymptotically
controllable time-varying systems},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {18},
PAGES = {1630--1641},
VOLUME = {72},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/albertini-clf.pdf},
ABSTRACT = { This paper shows that, for time varying systems, global
asymptotic controllability to a given closed subset of the state
space is equivalent to the existence of a continuous control-Lyapunov
function with respect to the set. }
}
@ARTICLE{MR1754903,
AUTHOR = {D. Angeli and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Forward completeness, unboundedness observability, and
their Lyapunov characterizations},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4-5},
PAGES = {209--217},
VOLUME = {38},
KEYWORDS = {observability, input to state stability,
dynamical systems},
PDF = {../../FTPDIR/uo.pdf},
ABSTRACT = { A finite-dimensional continuous-time system is forward
complete if solutions exist globally, for positive time. This paper
shows that forward completeness can be characterized in a necessary
and sufficient manner by means of smooth scalar growth inequalities.
Moreover, a version of this fact is also proved for systems with
inputs, and a generalization is also provided for systems with
outputs and a notion (unboundedness observability) of relative
completeness. We apply these results to obtain a bound on reachable
states in terms of energy-like estimates of inputs. }
}
@ARTICLE{MR1751688,
AUTHOR = {L. Grne and E.D. Sontag and F.R. Wirth},
JOURNAL = {Systems Control Lett.},
TITLE = {Asymptotic stability equals exponential stability, and
ISS equals finite energy gain---if you twist your eyes},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {127--134},
VOLUME = {38},
KEYWORDS = {input to state stability, ISS},
PDF = {../../FTPDIR/gas2ges.pdf},
ABSTRACT = { This paper shows that uniformly global asymptotic
stability for a family of ordinary differential equations is
equivalent to uniformly global exponential stability under a suitable
nonlinear change of variables. The same is shown respectively for
input-to-state stability, input-to-state exponential stability, and
the property of finite square-norm gain ("nonlinear H-infty"). The
results are shown for systems of any dimension not equal to 4 or 5. }
}
@ARTICLE{MR1695080,
AUTHOR = {Y.S. Ledyaev and E.D. Sontag},
JOURNAL = {Nonlinear Anal.},
TITLE = {A Lyapunov characterization of robust stabilization},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {7, Ser. A: Theory Methods},
PAGES = {813--840},
VOLUME = {37},
KEYWORDS = {nonlinear control, feedback stabilization},
PDF = {../../FTPDIR/yuri-clf.pdf},
ABSTRACT = { One of the fundamental facts in control theory
(Artstein's theorem) is the equivalence, for systems affine in
controls, between continuous feedback stabilizability to an
equilibrium and the existence of smooth control Lyapunov functions.
This equivalence breaks down for general nonlinear systems, not
affine in controls. One of the main results in this paper establishes
that the existence of smooth Lyapunov functions implies the existence
of (in general, discontinuous) feedback stabilizers which are
insensitive to small errors in state measurements. Conversely, it is
shown that the existence of such stabilizers in turn implies the
existence of smooth control Lyapunov functions. Moreover, it is
established that, for general nonlinear control systems under
persistently acting disturbances, the existence of smooth Lyapunov
functions is equivalent to the existence of (possibly) discontinuous)
feedback stabilizers which are robust with respect to small
measurement errors and small additive external disturbances. }
}
@ARTICLE{316387,
AUTHOR = {W. Maass and E.D. Sontag},
JOURNAL = {Neural Computation},
TITLE = {Analog neural nets with Gaussian or other common noise
distributions cannot recognize arbitrary regular languages},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {771--782},
VOLUME = {11},
ADDRESS = {Cambridge, MA, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PUBLISHER = {MIT Press},
PDF = {../../FTPDIR/maass_sontag_analog_neural_networks_gaussian_neural_computation1999.pdf},
ABSTRACT = { We consider recurrent analog neural nets where the
output of each gate is subject to Gaussian noise, or any other common
noise distribution that is nonzero on a large set. We show that many
regular languages cannot be recognized by networks of this type, and
we give a precise characterization of those languages which can be
recognized. This result implies severe constraints on possibilities
for constructing recurrent analog neural nets that are robust against
realistic types of analog noise. On the other hand we present a
method for constructing feedforward analog neural nets that are
robust with regard to analog noise of this type. },
DOI = {http://dx.doi.org/10.1162/089976699300016656}
}
@ARTICLE{MR1753276,
AUTHOR = {D. Nesic and A.R. Teel and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Formulas relating KL stability estimates of
discrete-time and sampled-data nonlinear systems},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {49--60},
VOLUME = {38},
KEYWORDS = {input to state stability, sampled-data systems,
discrete-time systems, sampling, ISS},
PDF = {../../FTPDIR/klsampling.pdf},
ABSTRACT = { We provide an explicit KL stability or input-to-state
stability (ISS) estimate for a sampled-data nonlinear system in terms
of the KL estimate for the corresponding discrete-time system and a K
function describing inter-sample growth. It is quite obvious that a
uniform inter-sample growth condition, plus an ISS property for the
exact discrete-time model of a closed-loop system, implies uniform
ISS of the sampled-data nonlinear system; our results serve to
quantify these facts by means of comparison functions. Our results
can be used as an alternative to prove and extend results of Aeyels
et al and extend some results by Chen et al to a class of nonlinear
systems. Finally, the formulas we establish can be used as a tool for
some other problems which we indicate. }
}
@ARTICLE{clocks99,
AUTHOR = {E.D. Sontag},
JOURNAL = {ESAIM Control Optim. Calc. Var.},
TITLE = {Clocks and insensitivity to small measurement errors},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {537--557},
VOLUME = {4},
KEYWORDS = {nonlinear control, feedback stabilization,
hybrid systems, discontinuous feedback, measurement noise},
PDF = {../../FTPDIR/clocks-sampling.pdf},
ABSTRACT = { This paper provides a precise result which shows that
insensitivity to small measurement errors in closed-loop
stabilization can be attained provided that the feedback controller
ignores observations during small time intervals. }
}
@ARTICLE{MR1750806,
AUTHOR = {E.D. Sontag and Y. Qiao},
JOURNAL = {Systems Control Lett.},
TITLE = {Further results on controllability of recurrent neural
networks},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {121--129},
VOLUME = {36},
KEYWORDS = {machine learning, artificial intelligence,
controllability, recurrent neural networks, neural networks},
PDF = {../../FTPDIR/qiao-scl.pdf},
ABSTRACT = { This paper studies controllability properties of
recurrent neural networks. The new contributions are: (1) an
extension of the result in "Complete controllability of
continuous-time recurrent neural networks" to a slightly different
model, where inputs appear in an affine form, (2) a formulation and
proof of a necessary and sufficient condition, in terms of
local-local controllability, and (3) a complete analysis of the
2-dimensional case for which the hypotheses made in previous work do
not apply. }
}
@ARTICLE{MR1754906,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {Systems Control Lett.},
TITLE = {Notions of input to output stability},
YEAR = {1999},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4-5},
PAGES = {235--248},
VOLUME = {38},
KEYWORDS = {input to state stability, ISS,
input to output stability},
PDF = {../../FTPDIR/ios.pdf},
ABSTRACT = { This paper deals with several related notions of output
stability with respect to inputs (which may be thought of as
disturbances). The main such notion is called input to output
stability (IOS), and it reduces to input to state stability (ISS)
when the output equals the complete state. For systems with no
inputs, IOS provides a generalization of the classical concept of
partial stability. Several variants, which formalize in different
manners the transient behavior, are introduced. The main results
provide a comparison among these notions }
}
@INPROCEEDINGS{99cdc-uo,
AUTHOR = {D. Angeli and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999},
TITLE = {Characterizations of forward completeness},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2551--2556},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{99cdc-gesgas,
AUTHOR = {L. Grune and E.D. Sontag and F.R. Wirth},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999},
TITLE = {On the equivalence between asymptotic and exponential
stability, and between ISS and finite H infinity gain},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1220--1225},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability}
}
@INPROCEEDINGS{99cdc-ios,
AUTHOR = {B.P. Ingalls and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999},
TITLE = {Remarks on input to output stability},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1226--1231},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, input to output stability}
}
@INPROCEEDINGS{99ifac,
AUTHOR = {Z-P. Jiang and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. 14th IFAC World Congress, Vol E (Beijing)},
TITLE = {Input-to-state stability for discrete-time nonlinear
systems},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {277--282},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, input to state stability, ISS,
discrete-time},
PDF = {../../FTPDIR/dt-iss-ifac.pdf},
ABSTRACT = { This paper studies the input-to-state stability (ISS)
property for discrete-time nonlinear systems. We show that many
standard ISS results may be extended to the discrete-time case. More
precisely, we provide a Lyapunov-like sufficient condition for ISS,
and we show the equivalence between the ISS property and various
other properties, as well as provide a small gain theorem. }
}
@INPROCEEDINGS{99cdc-ioss,
AUTHOR = {M. Krichman and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999},
TITLE = {Lyapunov characterizations of input-ouput-to-state
stability},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2070--2075},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS, detectability}
}
@INPROCEEDINGS{99acc-liberzon,
AUTHOR = {D. Liberzon and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999},
TITLE = {On integral-input-to-state stabilization},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1598--1602},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS,
control-Lyapunov functions},
PDF = {../../FTPDIR/99acc-liberzon-wang.pdf},
ABSTRACT = { This paper continues the investigation of the recently
introduced integral version of input-to-state stability (iISS). We
study the problem of designing control laws that achieve iISS
disturbance attenuation. The main contribution is an appropriate
concept of control Lyapunov function (iISS-CLF), whose existence
leads to an explicit construction of such a control law. The results
are compared and contrasted with the ones available for the ISS case. }
}
@INPROCEEDINGS{340649,
AUTHOR = {W. Maass and E.D. Sontag},
BOOKTITLE = {Proceedings of the 1998 conference on Advances in Neural Information Processing Systems II},
TITLE = {A precise characterization of the class of languages
recognized by neural nets under Gaussian and other common noise
distributions},
YEAR = {1999},
ADDRESS = {Cambridge, MA, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-11, Denver, 1998, https://papers.nips.cc/paper_files/paper/1998},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {281--287},
PUBLISHER = {MIT Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/98nips.pdf}
}
@INPROCEEDINGS{99acc-malissoff,
AUTHOR = {M. Malisoff and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999},
TITLE = {Universal formulas for CLF's with respect to Minkowski
balls},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3033--3037},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{99acc-nesic-teel,
AUTHOR = {D. Nesic and A.R. Teel and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conf., San Diego, June 1999},
TITLE = {On stability and input-to-state stability ${\cal K}{\cal
L}$ estimates of discrete-time and sampled-data nonlinear systems},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3990--3994},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, sampled-data systems,
discrete-time systems, sampling}
}
@INPROCEEDINGS{99cdc-clocks,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999},
TITLE = {Feedback insensitive to small measurement errors},
YEAR = {1999},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2661--2666},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@BOOK{mct,
PUBLISHER = {Springer-Verlag},
TITLE = {Mathematical Control Theory. Deterministic
Finite-Dimensional Systems},
YEAR = {1998},
AUTHOR = {E.D. Sontag},
ALTEDITOR = {},
ADDRESS = {New York},
EDITION = {Second},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
SERIES = {Texts in Applied Mathematics},
VOLUME = {6},
PAGES = {xvi+531},
PDF = {../../FTPDIR/sontag_mathematical_control_theory_springer98.pdf},
ABSTRACT = { This book is copyrighted by Springer-Verlag. Springer
has kindly allowed me to place a copy on the web, as a reference and
for ease of web searches. Please consider buying your own hardcopy. }
}
@INCOLLECTION{93ima_path_planning,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Essays on mathematical robotics (Minneapolis, MN, 1993)},
PUBLISHER = {Springer},
TITLE = {A general approach to path planning for systems without
drift},
YEAR = {1998},
ADDRESS = {New York},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {J. Baillieul and S. S. Sastry and H.J. Sussmann},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {151--168},
SERIES = {IMA Vol. Math. Appl.},
OPTTYPE = {},
VOLUME = {104},
KEYWORDS = {path-planning, systems without drift, nonlinear control,
controllability, real-analytic functions, gradient dynamics,
gradient descent, gradient systems, gradient descent,
numerical methods, dynamics of algorithms},
PDF = {../../FTPDIR/93ima_path_planning.pdf},
ABSTRACT = {This paper proposes a generally applicable technique for
the control of analytic systems with no drift. The method is based on
the generation of "nonsingular loops" that allow linearized
controllability. One can then implement Newton and/or gradient
searches in the search for a control. A general convergence theorem
is proved.}
}
@INCOLLECTION{303613,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {The handbook of brain theory and neural networks},
PUBLISHER = {MIT Press},
TITLE = {Automata and neural networks},
YEAR = {1998},
ADDRESS = {Cambridge, MA, USA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {119--122},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/98handbook_automata_neural_networks_preprint.pdf}
}
@INCOLLECTION{newtonVC,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Neural Networks and Machine Learning},
PUBLISHER = {Springer, Berlin},
TITLE = {VC dimension of neural networks},
YEAR = {1998},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C.M. Bishop},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {69-95},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence, VC dimension,
learning, neural networks, shattering},
PDF = {../../FTPDIR/vc-expo.pdf},
ABSTRACT = { The Vapnik-Chervonenkis (VC) dimension is an integer
which helps to characterize distribution-independent learning of
binary concepts from positive and negative samples. This paper, based
on lectures delivered at the Isaac Newton Institute in August of
1997, presents a brief introduction, establishes various elementary
results, and discusses how to estimate the VC dimension in several
examples of interest in neural network theory. (It does not address
the learning and estimation-theoretic applications of VC dimension,
and the applications to uniform convergence theorems for empirical
probabilities, for which many suitable references are available.) }
}
@ARTICLE{MR1634875,
AUTHOR = {P. Koiran and E.D. Sontag},
JOURNAL = {Discrete Applied Mathematics},
TITLE = {Vapnik-Chervonenkis dimension of recurrent neural
networks},
YEAR = {1998},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {63--79},
VOLUME = {86},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/koiran_sontag_vapnik-chervonenkis-dimension-of-recurrent_dam1998.pdf},
ABSTRACT = { This paper provides lower and upper bounds for the VC
dimension of recurrent networks. Several types of activation
functions are discussed, including threshold, polynomial,
piecewise-polynomial and sigmoidal functions. The bounds depend on
two independent parameters: the number w of weights in the network,
and the length k of the input sequence. Ignoring multiplicative
constants, the main results say roughly the following: 1. For
architectures whose activation is any fixed nonlinear polynomial, the
VC dimension is proportional to wk. 2. For architectures whose
activation is any fixed piecewise polynomial, the VC dimension is
between wk and w**2k. 3. For architectures with threshold
activations, the VC dimension is between wlog(k/w) and the smallest
of wklog(wk) and w**2+wlog(wk). 4. For the standard sigmoid tanh(x),
the VC dimension is between wk and w**4 k**2. },
DOI = {http://dx.doi.org/10.1016/S0166-218X(98)00014-6}
}
@ARTICLE{MR1749163,
AUTHOR = {D. Nesic and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Input-to-state stabilization of linear systems with
positive outputs},
YEAR = {1998},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {245--255},
VOLUME = {35},
KEYWORDS = {input to state stability, ISS, stabilization},
PDF = {../../FTPDIR/iss-sign-output.pdf},
ABSTRACT = {This paper considers the problem of stabilization of
linear systems for which only the magnitudes of outputs are measured.
It is shown that, if a system is controllable and observable, then
one can find a stabilizing controller, which is robust with respect
to observation noise (in the ISS sense). }
}
@ARTICLE{MR1632338,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A learning result for continuous-time recurrent neural
networks},
YEAR = {1998},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {151--158},
VOLUME = {34},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, recurrent neural networks},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/recur-learn.pdf},
ABSTRACT = { The following learning problem is considered, for
continuous-time recurrent neural networks having sigmoidal activation
functions. Given a ``black box'' representing an unknown system,
measurements of output derivatives are collected, for a set of
randomly generated inputs, and a network is used to approximate the
observed behavior. It is shown that the number of inputs needed for
reliable generalization (the sample complexity of the learning
problem) is upper bounded by an expression that grows polynomially
with the dimension of the network and logarithmically with the number
of output derivatives being matched. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(98)00006-1}
}
@ARTICLE{MR1629012,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Comments on integral variants of ISS},
YEAR = {1998},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1-2},
PAGES = {93--100},
VOLUME = {34},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/iiss.pdf},
ABSTRACT = { This note discusses two integral variants of the
input-to-state stability (ISS) property, which represent nonlinear
generalizations of L2 stability, in much the same way that ISS
generalizes L-infinity stability. Both variants are equivalent to ISS
for linear systems. For general nonlinear systems, it is shown that
one of the new properties is strictly weaker than ISS, while the
other one is equivalent to it. For bilinear systems, a complete
characterization is provided of the weaker property. An interesting
fact about functions of type KL is proved as well. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(98)00003-6}
}
@ARTICLE{MR1607810,
AUTHOR = {E.D. Sontag and F.R. Wirth},
JOURNAL = {Systems Control Lett.},
TITLE = {Remarks on universal nonsingular controls for
discrete-time systems},
YEAR = {1998},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {81--88},
VOLUME = {33},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {discrete time, controllability, real-analytic functions},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/wirth-scl.pdf},
ABSTRACT = { For analytic discrete-time systems, it is shown that
uniform forward accessibility implies the generic existence of
universal nonsingular control sequences. A particular application is
given by considering forward accessible systems on compact manifolds.
For general systems, it is proved that the complement of the set of
universal sequences of infinite length is of the first category. For
classes of systems satisfying a descending chain condition, and in
particular for systems defined by polynomial dynamics, forward
accessibility implies uniform forward accessibility. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00117-5}
}
@INPROCEEDINGS{98cdc-angeli-wang98,
AUTHOR = {D. Angeli and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {A remark on integral input to state stability},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2491--2496},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability}
}
@INPROCEEDINGS{98cdc-lin,
AUTHOR = {X. Bao and Z. Lin and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {Some new results on finite gain $l_p$ stabilization of
discrete-time linear systems subject to actuator saturation},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4628--4629},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs}
}
@INPROCEEDINGS{98cdc-dasgupta,
AUTHOR = {B. Dasgupta and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {A polynomial-time algorithm for an equivalence problem
which arises in hybrid systems theory},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1629--1634},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{98cdc-krichman,
AUTHOR = {M. Krichman and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {A version of a converse Lyapunov theorem for
input-output to state stability},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {4121--4126},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability}
}
@INPROCEEDINGS{98ciss-kuusela,
AUTHOR = {P. Kuusela and D. Ocone and E.D. Sontag},
BOOKTITLE = {Proc. 32nd Annual Conf. on Information Sciences and Systems (CISS 98), Princeton, NJ},
TITLE = {On the VC dimension of continuous-time linear control
systems},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {795--800},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{98acc-yuri,
AUTHOR = {Y.S. Ledyaev and E.D. Sontag},
BOOKTITLE = {Proc. American Control Conf., Philadelphia, June 1998},
TITLE = {Stabilization under measurement noise: Lyapunov
characterization},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1658--166},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{98cdc-nesic,
AUTHOR = {D. Nesic and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {Output stabilization of nonlinear systems: Linear
systems with positive outputs as a case study},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {885--890},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{98acc-iiss,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. American Control Conf., Philadelphia, June 1998},
TITLE = {Notions of integral input-to-state stability},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3215--321},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS}
}
@INPROCEEDINGS{98london,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Workshop on Control of Nonlinear and Uncertain Systems, London, Feb. 1998},
TITLE = {Recent results on discontinuous stabilization and
control-Lyapunov functions},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions}
}
@INPROCEEDINGS{98cdc-qiao,
AUTHOR = {E.D. Sontag and Y. Qiao},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998},
TITLE = {Remarks on controllability of recurrent neural networks},
YEAR = {1998},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {501--506},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks}
}
@INCOLLECTION{MR1476934,
AUTHOR = {P. Koiran and E.D. Sontag},
BOOKTITLE = {Computational learning theory (Jerusalem, 1997)},
PUBLISHER = {Springer-Verlag},
TITLE = {Vapnik-Chervonenkis dimension of recurrent neural
networks},
YEAR = {1997},
ADDRESS = {London, UK},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {223--237},
SERIES = {Lecture Notes in Comput. Sci.},
OPTTYPE = {},
VOLUME = {1208},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, recurrent neural networks}
}
@INCOLLECTION{MR1430107,
AUTHOR = {Y.S. Ledyaev and E.D. Sontag},
BOOKTITLE = {Control using logic-based switching (Block Island, RI, 1995)},
PUBLISHER = {Springer},
TITLE = {A notion of discontinuous feedback},
YEAR = {1997},
ADDRESS = {London},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {97--103},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {222}
}
@INCOLLECTION{recur-book-survey,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Dealing with Complexity: a Neural Network Approach},
PUBLISHER = {Springer-Verlag, London},
TITLE = {Recurrent neural networks: Some systems-theoretic
aspects},
YEAR = {1997},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {M. Karny and K. Warwick and V. Kurkova},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1--12},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks, learning, VC dimension},
PDF = {../../FTPDIR/recur-survey-book_as_published.pdf},
ABSTRACT = { This paper provides an exposition of some recent
results regarding system-theoretic aspects of continuous-time
recurrent (dynamic) neural networks with sigmoidal activation
functions. The class of systems is introduced and discussed, and a
result is cited regarding their universal approximation properties.
Known characterizations of controllability, observability, and
parameter identifiability are reviewed, as well as a result on
minimality. Facts regarding the computational power of recurrent nets
are also mentioned. }
}
@ARTICLE{clss97,
AUTHOR = {F. H. Clarke and Y.S. Ledyaev and E.D. Sontag and
A.I. Subbotin},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Asymptotic controllability implies feedback
stabilization},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {10},
PAGES = {1394--1407},
VOLUME = {42},
PDF = {../../FTPDIR/nonsmooth-feedback.pdf},
ABSTRACT = { It is shown that every asymptotically controllable
system can be stabilized by means of some (discontinuous) feedback
law. One of the contributions of the paper is in defining precisely
the meaning of stabilization when the feedback rule is not
continuous. The main ingredients in our construction are: (a) the
notion of control-Lyapunov function, (b) methods of nonsmooth
analysis, and (c) techniques from positional differential games. }
}
@ARTICLE{MR1437210,
AUTHOR = {M. J. Donahue and L. Gurvits and C. Darken and
E.D. Sontag},
JOURNAL = {Constr. Approx.},
TITLE = {Rates of convex approximation in non-Hilbert spaces},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {187--220},
VOLUME = {13},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, optimization, approximation theory},
PDF = {../../FTPDIR/ddgs.pdf},
ABSTRACT = { This paper deals with sparse approximations by means of
convex combinations of elements from a predetermined "basis" subset S
of a function space. Specifically, the focus is on the rate at which
the lowest achievable error can be reduced as larger subsets of S are
allowed when constructing an approximant. The new results extend
those given for Hilbert spaces by Jones and Barron, including in
particular a computationally attractive incremental approximation
scheme. Bounds are derived for broad classes of Banach spaces. The
techniques used borrow from results regarding moduli of smoothness in
functional analysis as well as from the theory of stochastic
processes on function spaces. }
}
@ARTICLE{MR1463259,
AUTHOR = {P. Koiran and E.D. Sontag},
JOURNAL = {J. Comput. System Sci.},
TITLE = {Neural networks with quadratic VC dimension},
YEAR = {1997},
OPTMONTH = {},
NOTE = {(1st Annual Dagstuhl Seminar on Neural Computing, 1994)},
NUMBER = {1, part 2},
PAGES = {190--198},
VOLUME = {54},
ADDRESS = {Orlando, FL, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension},
PUBLISHER = {Academic Press, Inc.},
PDF = {../../FTPDIR/quadratic-vc.pdf},
ABSTRACT = { This paper shows that neural networks which use
continuous activation functions have VC dimension at least as large
as the square of the number of weights w. This result settles the
open question of whether whether the well-known O(w log w) bound,
known for hard-threshold nets, also held for more general sigmoidal
nets. Implications for the number of samples needed for valid
generalization are discussed. },
DOI = {http://dx.doi.org/10.1006/jcss.1997.1479}
}
@ARTICLE{fourier-renee,
AUTHOR = {R. Koplon and E.D. Sontag},
JOURNAL = {Neurocomputing},
TITLE = {Using Fourier-neural recurrent networks to fit
sequential input/output data},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {225--248},
VOLUME = {15},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks},
PDF = {../../FTPDIR/fouriernet.pdf},
ABSTRACT = { This paper suggests the use of Fourier-type activation
functions in fully recurrent neural networks. The main theoretical
advantage is that, in principle, the problem of recovering internal
coefficients from input/output data is solvable in closed form. }
}
@ARTICLE{250973,
AUTHOR = {E.D. Sontag},
JOURNAL = {Neural Computation},
TITLE = {Shattering all sets of k points in `general position'
requires (k-1)/2 parameters},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {337--348},
VOLUME = {9},
ADDRESS = {Cambridge, MA, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, real-analytic functions},
PUBLISHER = {MIT Press},
PDF = {../../FTPDIR/generic.pdf},
ABSTRACT = { For classes of concepts defined by certain classes of
analytic functions depending on k parameters, there are nonempty open
sets of samples of length 2k+2 which cannot be shattered. A slighly
weaker result is also proved for piecewise-analytic functions. The
special case of neural networks is discussed. }
}
@ARTICLE{MR1455876,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
JOURNAL = {Systems Control Lett.},
TITLE = {Complete controllability of continuous-time recurrent
neural networks},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {177--183},
VOLUME = {30},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/reach-sigmoid.pdf},
ABSTRACT = { This paper presents a characterization of
controllability for the class of control systems commonly called
(continuous-time) recurrent neural networks. The characterization
involves a simple condition on the input matrix, and is proved when
the activation function is the hyperbolic tangent. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00002-9}
}
@ARTICLE{MR1432653,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {Systems Control Lett.},
TITLE = {Output-to-state stability and detectability of nonlinear
systems},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {279--290},
VOLUME = {29},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {input to state stability,
integral input to state stability, iISS, ISS, detectability,
output to state stability, detectability, input to state stability},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/oss_scl97.pdf},
ABSTRACT = { The notion of input-to-state stability (ISS) has proved
to be useful in nonlinear systems analysis. This paper discusses a
dual notion, output-to-state stability (OSS). A characterization is
provided in terms of a dissipation inequality involving storage
(Lyapunov) functions. Combining ISS and OSS there results the notion
of input/output-to-state stability (IOSS), which is also studied and
related to the notion of detectability, the existence of observers,
and output injection. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(97)90013-X}
}
@ARTICLE{MR1453841,
AUTHOR = {Y. Yang and E.D. Sontag and H.J. Sussmann},
JOURNAL = {Systems Control Lett.},
TITLE = {Global stabilization of linear discrete-time systems
with bounded feedback},
YEAR = {1997},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {273--281},
VOLUME = {30},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {discrete-time, saturation, bounded inputs},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/saturated-dt.pdf},
ABSTRACT = { This paper deals with the problem of global
stabilization of linear discrete time systems by means of bounded
feedback laws. The main result proved is an analog of one proved for
the continuous time case by the authors, and shows that such
stabilization is possible if and only if the system is stabilizable
with arbitrary controls and the transition matrix has spectral radius
less or equal to one. The proof provides in principle an algorithm
for the construction of such feedback laws, which can be implemented
either as cascades or as parallel connections (``single hidden layer
neural networks'') of simple saturation functions. },
DOI = {http://dx.doi.org/10.1016/S0167-6911(97)00021-2}
}
@INPROCEEDINGS{fa-clf,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. European Control Conf., Brussels, July 1997},
TITLE = {Control-Lyapunov functions for time-varying set
stabilization},
YEAR = {1997},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {(Paper WE-E A5, CD-ROM file ECC515.pdf, 6 pages)},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions}
}
@INPROCEEDINGS{97ciss-yuri,
AUTHOR = {Y.S. Ledyaev and E.D. Sontag},
BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997},
TITLE = {A remark on robust stabilization of general
asymptotically controllable systems},
YEAR = {1997},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {246--251},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/97ciss-robust.pdf},
ABSTRACT = { We showned in another recent paper that any
asymptotically controllable system can be stabilized by means of a
certain type of discontinuous feedback. The feedback laws constructed
in that work are robust with respect to actuator errors as well as to
perturbations of the system dynamics. A drawback, however, is that
they may be highly sensitive to errors in the measurement of the
state vector. This paper addresses this shortcoming, and shows how to
design a dynamic hybrid stabilizing controller which, while
preserving robustness to external perturbations and actuator error,
is also robust with respect to measurement error. This new design
relies upon a controller which incorporates an internal model of the
system driven by the previously constructed feedback. }
}
@INPROCEEDINGS{97ciss-nn,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 97), Johns Hopkins, Baltimore, MD, March 1997},
TITLE = {Some learning and systems-theoretic questions regarding
recurrent neural networks},
YEAR = {1997},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {630--635},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, recurrent neural networks}
}
@INPROCEEDINGS{ios-ecc,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. European Control Conf., Brussels, July 1997},
TITLE = {A notion of input to output stability},
YEAR = {1997},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {(Paper WE-E A2, CD-ROM file ECC958.pdf, 6 pages)},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS,
input to output stability, input to state stability},
PDF = {../../FTPDIR/97ecc-ios.pdf},
ABSTRACT = { This paper deals with a notion of "input to output
stability (IOS)", which formalizes the idea that outputs depend in an
"aymptotically stable" manner on inputs, while internal signals
remain bounded. When the output equals the complete state, one
recovers the property of input to state stability (ISS). When there
are no inputs, one has a generalization of the classical concept of
partial stability. The main results provide Lyapunov-function
characterizations of IOS. }
}
@BOOK{AHS,
PUBLISHER = {Springer Verlag, Berlin},
TITLE = {Hybrid Systems III. Verification and Control (edited
book)},
YEAR = {1996},
AUTHOR = {R. Alur and T.A. Henzinger and E.D. Sontag},
ALTEDITOR = {},
OPTADDRESS = {},
OPTEDITION = {},
OPTMONTH = {},
NOTE = {(LNCS 1066)},
OPTNUMBER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{PLS96dimacs,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control},
PUBLISHER = {Springer-Verlag New York, Inc.},
TITLE = {Interconnected automata and linear systems: a
theoretical framework in discrete-time},
YEAR = {1996},
ADDRESS = {Secaucus, NJ, USA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {R. Alur and T.A. Henzinger and E.D. Sontag},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {436--448},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {hybrid systems},
PDF = {../../FTPDIR/pls-expo.pdf},
ABSTRACT = { This paper summarizes the definitions and several of
the main results of an approach to hybrid systems, which combines
finite automata and linear systems, developed by the author in the
early 1980s. Some related more recent results are briefly mentioned
as well. }
}
@INCOLLECTION{MR1416368,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Stability theory (Ascona, 1995)},
PUBLISHER = {Birkhuser},
TITLE = {General classes of control-Lyapunov functions},
YEAR = {1996},
ADDRESS = {Basel},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {87--96},
SERIES = {Internat. Ser. Numer. Math.},
OPTTYPE = {},
VOLUME = {121},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/95hurwitzconf.pdf},
ABSTRACT = { Shorter and more expository version of "Nonsmooth
control-Lyapunov functions" }
}
@ARTICLE{TransInfoTheoVCperceptrons96,
AUTHOR = {B. DasGupta and E.D. Sontag},
JOURNAL = {IEEE Trans. Inform. Theory},
TITLE = {Sample complexity for learning recurrent perceptron
mappings},
YEAR = {1996},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {1479--1487},
VOLUME = {42},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, recurrent neural networks},
PDF = {../../FTPDIR/1996_dasgupta_sontag_learning_linear_systems.pdf},
ABSTRACT = { Recurrent perceptron classifiers generalize the usual
perceptron model. They correspond to linear transformations of input
vectors obtained by means of "autoregressive moving-average schemes",
or infinite impulse response filters, and allow taking into account
those correlations and dependences among input coordinates which
arise from linear digital filtering. This paper provides tight bounds
on sample complexity associated to the fitting of such models to
experimental data. The results are expressed in the context of the
theory of probably approximately correct (PAC) learning. }
}
@ARTICLE{MR1372908,
AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {A smooth converse Lyapunov theorem for robust stability},
YEAR = {1996},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {124--160},
VOLUME = {34},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {input to state stability},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/converse_siam_lin_sontag_wang_reprint_siam1996.pdf},
ABSTRACT = { This paper presents a Converse Lyapunov Function
Theorem motivated by robust control analysis and design. Our result
is based upon, but generalizes, various aspects of well-known
classical theorems. In a unified and natural manner, it (1) allows
arbitrary bounded time-varying parameters in the system description,
(2) deals with global asymptotic stability, (3) results in smooth
(infinitely differentiable) Lyapunov functions, and (4) applies to
stability with respect to not necessarily compact invariant sets. },
DOI = {http://dx.doi.org/10.1137/S0363012993259981}
}
@ARTICLE{MR1395830,
AUTHOR = {W. Liu and Y. Chitour and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {On finite-gain stabilizability of linear systems subject
to input saturation},
YEAR = {1996},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {1190--1219},
VOLUME = {34},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {saturation, bounded inputs},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/saturated_gains_liu_chitour_sontag_reprint_siam1996.pdf},
ABSTRACT = { This paper deals with (global) finite-gain input/output
stabilization of linear systems with saturated controls. For
neutrally stable systems, it is shown that the linear feedback law
suggested by the passivity approach indeed provides stability, with
respect to every Lp-norm. Explicit bounds on closed-loop gains are
obtained, and they are related to the norms for the respective
systems without saturation. These results do not extend to the class
of systems for which the state matrix has eigenvalues on the
imaginary axis with nonsimple (size >1) Jordan blocks, contradicting
what may be expected from the fact that such systems are globally
asymptotically stabilizable in the state-space sense; this is shown
in particular for the double integrator. },
DOI = {http://dx.doi.org/10.1137/S0363012994263469}
}
@ARTICLE{MR1399383,
AUTHOR = {E.D. Sontag},
JOURNAL = {Adv. Comput. Math.},
TITLE = {Critical points for least-squares problems involving
certain analytic functions, with applications to sigmoidal nets},
YEAR = {1996},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2-3},
PAGES = {245--268},
VOLUME = {5},
KEYWORDS = {machine learning, artificial intelligence,
subanalytic sets, semianalytic sets, critical points,
approximation theory, neural networks, real-analytic functions,
gradient dynamics, gradient descent, gradient systems,
gradient descent, numerical methods, dynamics of algorithms},
PDF = {../../FTPDIR/crit-sigmoid_reprint.pdf},
ABSTRACT = { This paper deals with nonlinear least-squares problems
involving the fitting to data of parameterized analytic functions.
For generic regression data, a general result establishes the
countability, and under stronger assumptions finiteness, of the set
of functions giving rise to critical points of the quadratic loss
function. In the special case of what are usually called
"single-hidden layer neural networks", which are built upon the
standard sigmoidal activation tanh(x) or equivalently 1/(1+exp(-x)),
a rough upper bound for this cardinality is provided as well. }
}
@ARTICLE{MR1409473,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {New characterizations of input-to-state stability},
YEAR = {1996},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {9},
PAGES = {1283--1294},
VOLUME = {41},
KEYWORDS = {input to state stability, ISS},
PDF = {../../FTPDIR/new-iss.pdf},
ABSTRACT = { We present new characterizations of the Input to State
Stability property. As a consequence of these results, we show the
equivalence between the ISS property and several (apparent)
variations proposed in the literature. }
}
@INPROCEEDINGS{ciss96cls,
AUTHOR = {F.H. Clarke and Y.S. Ledyaev and E.D. Sontag and
A.I. Subbotin},
BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 96)Princeton, NJ},
TITLE = {Asymptotic controllability and feedback stabilization},
YEAR = {1996},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1232--1237},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions, feedback stabilization}
}
@INPROCEEDINGS{dasgupta-nips,
AUTHOR = {B. Dasgupta and E.D. Sontag},
BOOKTITLE = {Advances in Neural Information Processing Systems 8},
TITLE = {Sample complexity for learning recurrent perceptron
mappings},
YEAR = {1996},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {D.S. Touretzky and M.C. Moser and M.E. Hasselmo},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-8, Denver, 1995, https://papers.nips.cc/paper_files/paper/1995},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {204--210},
PUBLISHER = {MIT Press, Cambridge, MA},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks, VC dimension, recurrent neural networks}
}
@INPROCEEDINGS{koiran-nips,
AUTHOR = {P. Koiran and E.D. Sontag},
BOOKTITLE = {Advances in Neural Information Processing Systems 8},
TITLE = {Neural networks with quadratic VC dimension},
YEAR = {1996},
OPTADDRESS = {},
OPTCROSSREF = {},
EDITOR = {D.S. Touretzky and M.C. Moser and M.E. Hasselmo},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-8, Denver, 1995, https://papers.nips.cc/paper_files/paper/1995},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {197--203},
PUBLISHER = {MIT Press, Cambridge, MA},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks, VC dimension}
}
@INPROCEEDINGS{ciss96,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ},
TITLE = {Detectability of nonlinear systems},
YEAR = {1996},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1031--1036},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {detectability, input to state stability, ISS},
PDF = {../../FTPDIR/oss.pdf},
ABSTRACT = { Contains a proof of a technical step, which was omitted
from the journal paper due to space constraints }
}
@TECHREPORT{bremen96,
AUTHOR = {E.D. Sontag and F.R. Wirth},
INSTITUTION = {Institute for Dynamical Systems, University of Bremen},
TITLE = {Remarks on universal nonsingular controls for
discrete-time systems},
YEAR = {1996},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {381},
OPTTYPE = {}
}
@INCOLLECTION{MR1326162,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Feedback control, nonlinear systems, and complexity (Montreal, PQ, 1994)},
PUBLISHER = {Springer},
TITLE = {State-space and i/o stability for nonlinear systems},
YEAR = {1995},
ADDRESS = {London},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {(Expository paper, placed online per request. The paper ``Input to state stability: Basic concepts and results'' is far more up to date and should be downloaded instead of this one!)},
OPTNUMBER = {},
PAGES = {215--235},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {202},
KEYWORDS = {input to state stability},
PDF = {../../FTPDIR/94montreal.pdf}
}
@INCOLLECTION{ControlHandbook,
AUTHOR = {A.R. Teel and T.T. Georgiou and L. Praly and E.D. Sontag},
BOOKTITLE = {The Control Handbook},
PUBLISHER = {CRC Press, Boca Raton},
TITLE = {Input-Output Stability},
YEAR = {1995},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {W. S. Levine},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {895--908},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/crc.pdf},
ABSTRACT = { An encyclopedia-type article on foundations of
input/output stability. }
}
@ARTICLE{MR1346408,
AUTHOR = {Y. Chitour and W. Liu and E.D. Sontag},
JOURNAL = {Internat. J. Robust Nonlinear Control},
TITLE = {On the continuity and incremental-gain properties of
certain saturated linear feedback loops},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {413--440},
VOLUME = {5},
KEYWORDS = {saturation, bounded inputs, incremental gains},
PDF = {../../FTPDIR/saturated-incr-gains.pdf},
ABSTRACT = { This paper discusses various continuity and
incremental-gain properties for neutrally stable linear systems under
linear feedback subject to actuator saturation. The results
complement our previous ones, which applied to the same class of
problems and provided finite-gain stability. }
}
@ARTICLE{MR1321019,
AUTHOR = {M. A. Dahleh and E.D. Sontag and D. N. C. Tse and
J. N. Tsitsiklis},
JOURNAL = {Automatica},
TITLE = {Worst-case identification of nonlinear fading memory
systems},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {503--508},
VOLUME = {31},
ADDRESS = {Tarrytown, NY, USA},
KEYWORDS = {information-based complexity, fading-memory systems,
stability, system identification, structured uncertainty},
PUBLISHER = {Pergamon Press, Inc.},
PDF = {../../FTPDIR/ibc-fading-mem.pdf},
ABSTRACT = { We consider the problem of characterizing possible
supply functions for a given dissipative nonlinear system, and
provide a result that allows some freedom in the modification of such
functions. },
DOI = {http://dx.doi.org/10.1016/0005-1098(94)00131-2}
}
@ARTICLE{DasGupta-TNN,
AUTHOR = {B. DasGupta and H.T. Siegelmann and E.D. Sontag},
JOURNAL = {IEEE Trans. Neural Networks},
TITLE = {On the complexity of training neural networks with
continuous activation functions},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1490--1504},
VOLUME = {6},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, analog computing, theory of computing,
neural networks, computational complexity, machine learning},
PDF = {../../FTPDIR/complexity-training.pdf},
ABSTRACT = { Blum and Rivest showed that any possible neural net
learning algorithm based on fixed architectures faces severe
computational barriers. This paper extends their NP-completeness
result, which applied only to nets based on hard threshold
activations, to nets that employ a particular continuous activation.
In view of neural network practice, this is a more relevant result to
understanding the limitations of backpropagation and related
techniques. }
}
@ARTICLE{MR1424371,
AUTHOR = {Y. Lin and E.D. Sontag},
JOURNAL = {Control Theory and Advanced Technology},
TITLE = {Control-Lyapunov universal formulas for restricted
inputs},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4, part 5},
PAGES = {1981--2004},
VOLUME = {10},
KEYWORDS = {control-Lyapunov functions, saturation, bounded inputs},
PDF = {../../FTPDIR/clf-bounded-ctat_reprint.pdf},
ABSTRACT = { We deal with the question of obtaining explicit
feedback control laws that stabilize a nonlinear system, under the
assumption that a "control Lyapunov function" is known. In previous
work, the case of unbounded controls was considered. Here we obtain
results for bounded and/or positive controls. We also provide some
simple preliminary remarks regarding a set stability version of the
problem and a version for systems subject to disturbances. }
}
@ARTICLE{MR1329624,
AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang},
JOURNAL = {Internat. J. Robust Nonlinear Control},
TITLE = {Input to state stabilizability for parametrized families
of systems},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {187--205},
VOLUME = {5},
KEYWORDS = {ISS, stabilization},
PDF = {../../FTPDIR/issparametric.pdf},
ABSTRACT = { This paper studies various stability issues for
parameterized families of systems, including problems of
stabilization with respect to sets. The study of such families is
motivated by robust control applications. A Lyapunov-theoretic
necessary and sufficient characterization is obtained for a natural
notion of robust uniform set stability; this characterization allows
replacing ad hoc conditions found in the literature by more
conceptual stability notions. We then use these techniques to
establish a result linking state space stability to ``input to
state'' (bounded-input bounded-state) stability. In addition, the
preservation of stabilizability under certain types of cascade
interconnections is analyzed. }
}
@ARTICLE{MR1322637,
AUTHOR = {H. T. Siegelmann and E.D. Sontag},
JOURNAL = {J. Computer System Sciences},
TITLE = {On the computational power of neural nets},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {132--150},
VOLUME = {50},
ADDRESS = {Orlando, FL, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks, machine learning,
analog computing, theory of computing, neural networks,
computational complexity, super-Turing computation},
PUBLISHER = {Academic Press, Inc.},
PDF = {../../FTPDIR/siegelmann_sontag_jcss1995.pdf},
ABSTRACT = { This paper deals with finite size networks which
consist of interconnections of synchronously evolving processors.
Each processor updates its state by applying a "sigmoidal" function
to a rational-coefficient linear combination of the previous states
of all units. We prove that one may simulate all Turing Machines by
such nets. In particular, one can simulate any multi-stack Turing
Machine in real time, and there is a net made up of 886 processors
which computes a universal partial-recursive function. Products (high
order nets) are not required, contrary to what had been stated in the
literature. Non-deterministic Turing Machines can be simulated by
non-deterministic rational nets, also in real time. The simulation
result has many consequences regarding the decidability, or more
generally the complexity, of questions about recursive nets. },
DOI = {http://dx.doi.org/10.1006/jcss.1995.1013}
}
@ARTICLE{MR1344033,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Control of systems without drift via generic loops},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {7},
PAGES = {1210--1219},
VOLUME = {40},
KEYWORDS = {stabilization, non-holonomic systems, path-planning,
systems without drift, nonlinear control, controllability,
real-analytic functions},
PDF = {../../FTPDIR/nonsing-loop.pdf},
ABSTRACT = {This paper proposes a simple numerical technique for the
steering of arbitrary analytic systems with no drift. It is based on
the generation of "nonsingular loops" which allow linearized
controllability along suitable trajetories. Once such loops are
available, it is possible to employ standard Newton or steepest
descent methods, as classically done in numerical control. The
theoretical justification of the approach relies on recent results
establishing the genericity of nonsingular controls, as well as a
simple convergence lemma. }
}
@ARTICLE{iss-ejc,
AUTHOR = {E.D. Sontag},
JOURNAL = {European J. Control},
TITLE = {On the input-to-state stability property},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {24--36},
VOLUME = {1},
KEYWORDS = {input to state stability, ISS},
PDF = {../../FTPDIR/1995_sontag_iss_ejc_reprint.pdf},
ABSTRACT = { The "input to state stability" (ISS) property provides
a natural framework in which to formulate notions of stability with
respect to input perturbations. In this expository paper, we review
various equivalent definitions expressed in stability,
Lyapunov-theoretic, and dissipation terms. We sketch some
applications to the stabilization of cascades of systems and of
linear systems subject to control saturation. }
}
@ARTICLE{MR1343820,
AUTHOR = {E.D. Sontag and A.R. Teel},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Changing supply functions in input/state stable systems},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {8},
PAGES = {1476--1478},
VOLUME = {40},
KEYWORDS = {input to state stability, ISS, input to state stability,
Lyapunov functions},
PDF = {../../FTPDIR/tn950112.pdf},
ABSTRACT = {We consider the problem of characterizing possible
supply functions for a given dissipative nonlinear system, and
provide a result that allows some freedom in the modification of such
functions. }
}
@ARTICLE{MR1325675,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {Systems Control Lett.},
TITLE = {On characterizations of the input-to-state stability
property},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {351--359},
VOLUME = {24},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {input to state stability, ISS},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/converse-iss.pdf},
ABSTRACT = { We show that the well-known Lyapunov sufficient
condition for input-to-state stability is also necessary, settling
positively an open question raised by several authors during the past
few years. Additional characterizations of the ISS property,
including one in terms of nonlinear stability margins, are also
provided. },
DOI = {http://dx.doi.org/10.1016/0167-6911(94)00050-6}
}
@ARTICLE{MR1339057,
AUTHOR = {Y. Wang and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Orders of input/output differential equations and
state-space dimensions},
YEAR = {1995},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {1102--1126},
VOLUME = {33},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {identifiability, observability, realization theory,
real-analytic functions},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/orders_ioequations_state_space_dimensions_wang_sontag_reprint_siam1995.pdf},
ABSTRACT = { This paper deals with the orders of input/output
equations satisfied by nonlinear systems. Such equations represent
differential (or difference, in the discrete-time case) relations
between high-order derivatives (or shifts, respectively) of input and
output signals. It is shown that, under analyticity assumptions,
there cannot exist equations of order less than the minimal dimension
of any observable realization; this generalizes the known situation
in the classical linear case. The results depend on new facts,
themselves of considerable interest in control theory, regarding
universal inputs for observability in the discrete case, and
observation spaces in both the discrete and continuous cases.
Included in the paper is also a new and simple self-contained proof
of Sussmann's universal input theorem for continuous-time analytic
systems. },
DOI = {http://dx.doi.org/10.1137/S0363012993246828}
}
@INPROCEEDINGS{95cdc-diss,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995},
TITLE = {An abstract approach to dissipation},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Full version, never submitted, is here: http://sontaglab.org/FTPDIR/dissipation.pdf},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2702--2703},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {quasimetric spaces, dissipative systems,
nonlinear systems},
PDF = {../../FTPDIR/95cdc-diss.pdf},
ABSTRACT = { We suggest that a very natural mathematical framework
for the study of dissipation -in the sense of Willems, Moylan and
Hill, and others- is that of indefinite quasimetric spaces. Several
basic facts about dissipative systems are seen to be simple
consequences of the properties of such spaces. Quasimetric spaces
provide also one natural context for optimal control problems, and
even for "gap" formulations of robustness. }
}
@INPROCEEDINGS{95icnn,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. 1995 IEEE Internat. Conf. Neural Networks, IEEE Publications, 1995},
TITLE = {Critical points for neural net least-squares problems},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2949--2954},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks}
}
@INPROCEEDINGS{95cdc-complexity,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995},
TITLE = {From linear to nonlinear: some complexity comparisons},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2916--2920},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {theory of computing and complexity,
computational complexity, controllability, observability},
PDF = {../../FTPDIR/95cdc-complexity.pdf},
ABSTRACT = { This paper deals with the computational complexity, and
in some cases undecidability, of several problems in nonlinear
control. The objective is to compare the theoretical difficulty of
solving such problems to the corresponding problems for linear
systems. In particular, the problem of null-controllability for
systems with saturations (of a "neural network" type) is mentioned,
as well as problems regarding piecewise linear (hybrid) systems. A
comparison of accessibility, which can be checked fairly simply by
Lie-algebraic methods, and controllability, which is at least NP-hard
for bilinear systems, is carried out. Finally, some remarks are given
on analog computation in this context. }
}
@INPROCEEDINGS{icm94,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zrich, 1994)},
TITLE = {Spaces of observables in nonlinear control},
YEAR = {1995},
ADDRESS = {Basel},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1532--1545},
PUBLISHER = {Birkhuser},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {observability, dynamical systems},
PDF = {../../FTPDIR/icm.pdf},
ABSTRACT = { Invited talk at the 1994 ICM. Paper deals with the
notion of observables for nonlinear systems, and their role in
realization theory, minimality, and several control and path planning
questions. }
}
@INPROCEEDINGS{95cdc-hs,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995},
TITLE = {Nonsmooth control-Lyapunov functions},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2799--2805},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/95cdc-clf.pdf},
ABSTRACT = { It is shown that the existence of a continuous
control-Lyapunov function (CLF) is necessary and sufficient for null
asymptotic controllability of nonlinear finite-dimensional control
systems. The CLF condition is expressed in terms of a concept of
generalized derivative (upper contingent derivative). This result
generalizes to the non-smooth case the theorem of Artstein relating
closed-loop feedback stabilization to smooth CLF's. It relies on
viability theory as well as optimal control techniques. A
"non-strict" version of the results, analogous to the LaSalle
Invariance Principle, is also provided. }
}
@INPROCEEDINGS{95nolcos,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, June 1995},
TITLE = {On characterizations of input-to-state stability with
respect to compact sets},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {226--231},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS},
PDF = {../../FTPDIR/95nolcos.pdf},
ABSTRACT = { Previous characterizations of ISS-stability are shown
to generalize without change to the case of stability with respect to
sets. Some results on ISS-stabilizability are mentioned as well. }
}
@INPROCEEDINGS{95cdc-yw,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995},
TITLE = {Various results concerning set input-to-state stability},
YEAR = {1995},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1330--1335},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS}
}
@INCOLLECTION{DasGupta-book,
AUTHOR = {B. DasGupta and H.T. Siegelmann and E.D. Sontag},
BOOKTITLE = {Theoretical Advances in Neural Computation and Learning},
PUBLISHER = {Kluwer Academic Publishers},
TITLE = {On the Intractability of Loading Neural Networks},
YEAR = {1994},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {V. P. Roychowdhury and Siu K. Y. and Orlitsky A.},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {357--389},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity,
machine learning},
PDF = {../../FTPDIR/dasgupta_siegelmann_sontag_intractability_loading_neural_networks_bookchapter_springer1994.pdf}
}
@INCOLLECTION{maass-schnitger-book,
AUTHOR = {W. Maass and G. Schnitger and E.D. Sontag},
BOOKTITLE = {Theoretical Advances in Neural Computation and Learning},
PUBLISHER = {Kluwer Academic Publishers},
TITLE = {A comparison of the computational power of sigmoid and
Boolean threshold circuits},
YEAR = {1994},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {V. P. Roychowdhury and Siu K. Y. and Orlitsky A.},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {127--151},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, boolean systems},
PDF = {../../FTPDIR/maass_schnitger_sontag_comparison_sigmoid_boolean_springer1994.pdf},
ABSTRACT = { We examine the power of constant depth circuits with
sigmoid threshold gates for computing boolean functions. It is shown
that, for depth 2, constant size circuits of this type are strictly
more powerful than constant size boolean threshold circuits (i.e.
circuits with linear threshold gates). On the other hand it turns out
that, for any constant depth d, polynomial size sigmoid threshold
circuits with polynomially bounded weights compute exactly the same
boolean functions as the corresponding circuits with linear threshold
gates. }
}
@ARTICLE{MR1298518,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {Dynam. Control},
TITLE = {Further results on controllability properties of
discrete-time nonlinear systems},
YEAR = {1994},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {235--253},
VOLUME = {4},
ADDRESS = {Hingham, MA, USA},
KEYWORDS = {discrete-time, nonlinear control},
PUBLISHER = {Kluwer Academic Publishers},
PDF = {../../FTPDIR/dt_further_albertini_sontag_reprint_dynamics_and_control1994.pdf},
ABSTRACT = { Controllability questions for discrete-time nonlinear
systems are addressed in this paper. In particular, we continue the
search for conditions under which the group-like notion of
transitivity implies the stronger and semigroup-like property of
forward accessibility. We show that this implication holds,
pointwise, for states which have a weak Poisson stability property,
and globally, if there exists a global "attractor" for the system. },
DOI = {http://dx.doi.org/10.1007/BF01985073}
}
@ARTICLE{MR1270887,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {State observability in recurrent neural networks},
YEAR = {1994},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {235--244},
VOLUME = {22},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks, observability,
identifiability},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/obs-sigma.pdf},
ABSTRACT = { This paper concerns recurrent networks x'=s(Ax+Bu),
y=Cx, where s is a sigmoid, in both discrete time and continuous
time. Our main result is that observability can be characterized, if
one assumes certain conditions on the nonlinearity and on the system,
in a manner very analogous to that of the linear case. Recall that
for the latter, observability is equivalent to the requirement that
there not be any nontrivial A-invariant subspace included in the
kernel of C. We show that the result generalizes in a natural manner,
except that one now needs to restrict attention to certain special
"coordinate" subspaces. },
DOI = {http://dx.doi.org/10.1016/0167-6911(94)90054-X}
}
@ARTICLE{MR1276846,
AUTHOR = {R. Koplon and E.D. Sontag and M. L. J. Hautus},
JOURNAL = {Linear Algebra Appl.},
TITLE = {Observability of linear systems with saturated outputs},
YEAR = {1994},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {909--936},
VOLUME = {205/206},
KEYWORDS = {observability, saturation, bounded inputs},
PDF = {../../FTPDIR/outputsat.pdf},
ABSTRACT = { In this paper, we present necessary and sufficient
conditions for observability of the class of output-saturated
systems. These are linear systems whose output passes through a
saturation function before it can be measured. }
}
@ARTICLE{MR1288945,
AUTHOR = {H. T. Siegelmann and E.D. Sontag},
JOURNAL = {Theoretical Computer Science},
TITLE = {Analog computation via neural networks},
YEAR = {1994},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {331--360},
VOLUME = {131},
ADDRESS = {Essex, UK},
KEYWORDS = {analog computing, neural networks,
computational complexity, super-Turing computation,
recurrent neural networks, machine learning, artificial intelligence,
neural networks, computational complexity},
PUBLISHER = {Elsevier Science Publishers Ltd.},
PDF = {../../FTPDIR/siegelmann_sontag_tcs1994.pdf},
ABSTRACT = { We consider recurrent networks with real-valued
weights. If allowed exponential time for computation, they turn out
to have unbounded power. However, under polynomial-time constraints
there are limits on their capabilities, though being more powerful
than Turing Machines. Moreover, there is a precise correspondence
between nets and standard non-uniform circuits with equivalent
resources, and as a consequence one has lower bound constraints on
what they can compute. We note that these networks are not likely to
solve polynomially NP-hard problems, as the equality "P=NP" in our
model implies the almost complete collapse of the standard polynomial
hierarchy. We show that a large class of different networks and
dynamical system models have no more computational power than this
neural (first-order) model with real weights. The results suggest the
following Church-like Thesis of Time-bounded Analog Computing: "Any
reasonable analog computer will have no more power (up to polynomial
time) than first-order recurrent networks." },
DOI = {http://dx.doi.org/10.1016/0304-3975(94)90178-3}
}
@ARTICLE{MR1337566,
AUTHOR = {H.J. Sussmann and E.D. Sontag and Y. Yang},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {A general result on the stabilization of linear systems
using bounded controls},
YEAR = {1994},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {12},
PAGES = {2411--2425},
VOLUME = {39},
KEYWORDS = {saturation, neural networks, global stability,
nonlinear stability, bounded inputs},
PDF = {../../FTPDIR/saturated-stab.pdf},
ABSTRACT = { We present two constructions of controllers that
globally stabilize linear systems subject to control saturation. We
allow essentially arbitrary saturation functions. The only conditions
imposed on the system are the obvious necessary ones, namely that no
eigenvalues of the uncontrolled system have positive real part and
that the standard stabilizability rank condition hold. One of the
constructions is in terms of a "neural-network type" one-hidden layer
architecture, while the other one is in terms of cascades of linear
maps and saturations. }
}
@INPROCEEDINGS{94cdc-saturated,
AUTHOR = {Y. Chitour and W. Liu and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994},
TITLE = {On the continuity and incremental gain properties of
certain saturated linear feedback loops},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {127--132},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs},
PDF = {../../FTPDIR/94cdc-saturated.pdf}
}
@INPROCEEDINGS{181009,
AUTHOR = {B. DasGupta and H. T. Siegelmann and E.D. Sontag},
BOOKTITLE = {COLT '94: Proceedings of the seventh annual conference on Computational learning theory},
TITLE = {On a learnability question associated to neural networks
with continuous activations (extended abstract)},
YEAR = {1994},
ADDRESS = {New York, NY, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {47--56},
PUBLISHER = {ACM Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity},
DOI = {http://doi.acm.org/10.1145/180139.181009}
}
@INPROCEEDINGS{94cdc-renee,
AUTHOR = {R. Koplon and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994},
TITLE = {Techniques for parameter reconstruction in
Fourier-Neural recurrent networks},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {213--218},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks}
}
@INPROCEEDINGS{94cdc-clf,
AUTHOR = {Y. Lin and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994},
TITLE = {On control-Lyapunov functions under input constraints},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {640--645},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions}
}
@INPROCEEDINGS{94acc,
AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. Amer. Automatic Control Conf., Baltimore, June 1994},
TITLE = {Recent results on Lyapunov-theoretic techniques for
nonlinear stability},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1771--1775},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{94cdc-iss,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994},
TITLE = {Notions equivalent to input-to-state stability},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3438--3443},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS}
}
@INPROCEEDINGS{94cdc-univ,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994},
TITLE = {Orders of I/O equations and uniformly universal inputs},
YEAR = {1994},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1270--1275},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identifiability, observability, realization theory}
}
@INCOLLECTION{92caip,
AUTHOR = {F. Albertini and E.D. Sontag and V. Maillot},
BOOKTITLE = {Artificial Neural Networks for Speech and Vision},
PUBLISHER = {Chapman and Hall, London},
TITLE = {Uniqueness of weights for neural networks},
YEAR = {1993},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {R. Mammone},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {115--125},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks},
PDF = {../../FTPDIR/92caip.pdf},
ABSTRACT = { In this short expository survey, we sketch various
known facts about uniqueness of weights in neural networks, including
results about recurrent nets, and we provide a new and elementary
complex-variable proof of a uniqueness result that applies in the
single hidden layer case. }
}
@INCOLLECTION{MR1247275,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Essays on control: perspectives in the theory and its applications (Groningen, 1993)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Neural networks for control},
YEAR = {1993},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {H. L. Trentelman and J. C. Willems},
OPTMONTH = {},
NOTE = {A longer version (tech report with more details) is here: http://sontaglab.org/FTPDIR/neural-nets-siemens.pdf},
OPTNUMBER = {},
PAGES = {339--380},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {14},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks, machine learning,
neural networks},
PDF = {../../FTPDIR/93ecc-nn.pdf},
ABSTRACT = { This paper has an expository introduction to two
related topics: (a) Some mathematical results regarding "neural
networks", and (b) so-called "neurocontrol" and "learning control"
(each part can be read independently of the other). It was prepared
for a short course given at the 1993 European Control Conference. },
DOI = {https://doi.org/10.1007/978-1-4612-0313-1_10}
}
@INCOLLECTION{robot86reprint,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Robot Control},
PUBLISHER = {IEEE Press, New York},
TITLE = {Time-optimal control of manipulators (reprint of 1986
IEEE Int Conf on Robotics and Automation paper},
YEAR = {1993},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {M.W. Spong and F.L. Lewis and C.T. Abdallah},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {266--271},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {robotics, optimal control}
}
@ARTICLE{MR1242218,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Discrete-time transitivity and accessibility: analytic
systems},
YEAR = {1993},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {1599--1622},
VOLUME = {31},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {controllability, discrete-time systems, accessibility,
real-analytic functions},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/dt-analytic-albertini_reprint_siam1993.pdf},
ABSTRACT = { A basic open question for discrete-time nonlinear
systems is that of determining when, in analogy with the classical
continuous-time "positive form of Chow's Lemma", accessibility
follows from transitivity of a natural group action. This paper
studies the problem, and establishes the desired implication for
analytic systems in several cases: (i) compact state space, (ii)
under a Poisson stability condition, and (iii) in a generic sense. In
addition, the paper studies accessibility properties of the "control
sets" recently introduced in the context of dynamical systems
studies. Finally, various examples and counterexamples are provided
relating the various Lie algebras introduced in past work. },
DOI = {http://dx.doi.org/10.1137/0331075}
}
@ARTICLE{165043,
AUTHOR = {F. Albertini and E.D. Sontag},
JOURNAL = {Neural Networks},
TITLE = {For neural networks, function determines form},
YEAR = {1993},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {7},
PAGES = {975--990},
VOLUME = {6},
ADDRESS = {Oxford, UK, UK},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, identifiability, recurrent neural networks,
realization theory, observability, neural networks},
PUBLISHER = {Elsevier Science Ltd.},
PDF = {../../FTPDIR/net-ident.pdf},
ABSTRACT = { This paper shows that the weights of continuous-time
feedback neural networks x'=s(Ax+Bu), y=Cx (where s is a sigmoid) are
uniquely identifiable from input/output measurements. Under very weak
genericity assumptions, the following is true: Assume given two nets,
whose neurons all have the same nonlinear activation function s; if
the two nets have equal behaviors as "black boxes" then necessarily
they must have the same number of neurons and -except at most for
sign reversals at each node- the same weights. Moreover, even if the
activations are not a priori known to coincide, they are shown to be
also essentially determined from the external measurements. }
}
@ARTICLE{MR1234002,
AUTHOR = {R. Koplon and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Linear systems with sign-observations},
YEAR = {1993},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {1245--1266},
VOLUME = {31},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {observability},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/signlinear_koplon_sontag_repreint_siam1993.pdf},
ABSTRACT = { This paper deals with systems that are obtained from
linear time-invariant continuous- or discrete-time devices followed
by a function that just provides the sign of each output. Such
systems appear naturally in the study of quantized observations as
well as in signal processing and neural network theory. Results are
given on observability, minimal realizations, and other
system-theoretic concepts. Certain major differences exist with the
linear case, and other results generalize in a surprisingly
straightforward manner. },
DOI = {http://dx.doi.org/10.1137/0331059}
}
@INPROCEEDINGS{fa-93mtns1,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg},
TITLE = {Controllability of discrete-time nonlinear systems},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {35--38},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{fa-93ecc,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. European Control Conf., Groningen, June 1993},
TITLE = {Identifiability of discrete-time neural networks},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {460--465},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks}
}
@INPROCEEDINGS{93cdc-obs-sigma,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {State observability in recurrent neural networks},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3706--3707},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, observability, recurrent neural networks}
}
@INPROCEEDINGS{fa-93mtns2,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Systems and Networks: Mathematical Theory and Applications, Proc. MTNS '93, Vol. 2, Akad. Verlag, Regensburg},
TITLE = {Uniqueness of weights for recurrent nets},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Full version, never submitted for publication, is here: http://sontaglab.org/FTPDIR/93mtns-nn-extended.pdf},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {599--602},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, identifiability, recurrent neural networks},
PDF = {../../FTPDIR/93mtns-nn.pdf},
ABSTRACT = { This paper concerns recurrent networks x'=s(Ax+Bu),
y=Cx, where s is a sigmoid, in both discrete time and continuous
time. The paper establishes parameter identifiability under stronger
assumptions on the activation than in "For neural networks, function
determines form", but on the other hand deals with arbitrary
(nonzero) initial states. }
}
@INPROCEEDINGS{MR1310805,
AUTHOR = {J. L. Balczar and R. Gavald and H. T. Siegelmann and
E.D. Sontag},
BOOKTITLE = {Proceedings of the Eighth Annual Structure in Complexity Theory Conference (San Diego, CA, 1993)},
TITLE = {Some structural complexity aspects of neural computation},
YEAR = {1993},
ADDRESS = {Los Alamitos, CA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {253--265},
PUBLISHER = {IEEE Comput. Soc. Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity,
super-Turing computation, theory of computing and complexity},
PDF = {../../FTPDIR/balcazar_gavalda_siegelmann_sontag_structural_complexity_neural_computation_1993_structure_complexity_conference.pdf},
ABSTRACT = {Recent work by H.T. Siegelmann and E.D. Sontag (1992)
has demonstrated that polynomial time on linear saturated recurrent
neural networks equals polynomial time on standard computational
models: Turing machines if the weights of the net are rationals, and
nonuniform circuits if the weights are real. Here, further
connections between the languages recognized by such neural nets and
other complexity classes are developed. Connections to space-bounded
classes, simulation of parallel computational models such as Vector
Machines, and a discussion of the characterizations of various
nonuniform classes in terms of Kolmogorov complexity are presented.}
}
@INPROCEEDINGS{168357,
AUTHOR = {C. Darken and M.J. Donahue and L. Gurvits and
E.D. Sontag},
BOOKTITLE = {COLT '93: Proceedings of the sixth annual conference on Computational learning theory},
TITLE = {Rate of approximation results motivated by robust neural
network learning},
YEAR = {1993},
ADDRESS = {New York, NY, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {303--309},
PUBLISHER = {ACM Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
machine learning, neural networks, optimization problems,
approximation theory},
DOI = {http://doi.acm.org/10.1145/168304.168357}
}
@INPROCEEDINGS{93cdc-renee,
AUTHOR = {R. Koplon and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {Sign-linear systems as cascades of automata and
continuous variable systems},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2290--2291},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{93cdc-gerardo,
AUTHOR = {G.A. Lafferriere and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {Remarks on control Lyapunov functions for discontinuous
stabilizing feedback},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {306--308},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {feedback stabilization},
PDF = {../../FTPDIR/93cdc-clf.pdf},
ABSTRACT = { We present a formula for a stabilizing feedback law
under the assumption that a piecewise smooth control-Lyapunov
function exists. The resulting feedback is continuous at the origin
and smooth everywhere except on a hypersurface of codimension 1,
assuming that certain transversality conditions are imposed there. }
}
@INPROCEEDINGS{93cdc-yuandan,
AUTHOR = {Y. Lin and E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {Lyapunov-function characterizations of stability and
stabilization for parameterized families of systems},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1978--1983},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{93cdc-liu,
AUTHOR = {W. Liu and Y. Chitour and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {Remarks on finite gain stabilizability of linear systems
subject to input saturation},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1808--1813},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs}
}
@INPROCEEDINGS{167192,
AUTHOR = {A. Macintyre and E.D. Sontag},
BOOKTITLE = {STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing},
TITLE = {Finiteness results for sigmoidal neural networks},
YEAR = {1993},
ADDRESS = {New York, NY, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {325--334},
PUBLISHER = {ACM Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, theory of computing and complexity,
real-analytic functions},
PDF = {../../FTPDIR/ajm.pdf},
ABSTRACT = { This paper deals with analog circuits. It establishes
the finiteness of VC dimension, teaching dimension, and several other
measures of sample complexity which arise in learning theory. It also
shows that the equivalence of behaviors, and the loading problem, are
effectively decidable, modulo a widely believed conjecture in number
theory. The results, the first ones that are independent of weight
size, apply when the gate function is the "standard sigmoid" commonly
used in neural networks research. The proofs rely on very recent
developments in the elementary theory of real numbers with
exponentiation. (Some weaker conclusions are also given for more
general analytic gate functions.) Applications to learnability of
sparse polynomials are also mentioned. },
DOI = {http://doi.acm.org/10.1145/167088.167192}
}
@INPROCEEDINGS{93israel-hava,
AUTHOR = {H.T. Siegelmann and E.D. Sontag},
BOOKTITLE = {Proc. 2nd Israel Symposium on Theory of Computing and Systems (ISTCS93), IEEE Computer Society Press, 1993},
TITLE = {Analog computation via neural networks},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity,
super-Turing computation, recurrent neural networks}
}
@INPROCEEDINGS{93cdc-pathplanning,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {Gradient techniques for systems with no drift: A
classical idea revisited},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2706--2711},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {path-planning, systems without drift, nonlinear control,
controllability, real-analytic functions, gradient dynamics,
gradient descent, gradient systems, gradient descent,
numerical methods, dynamics of algorithms},
PDF = {../../FTPDIR/93cdc-pathplanning.pdf},
ABSTRACT = {This paper proposes a technique for the control of
analytic systems with no drift. It is based on the generation of
"nonsingular loops" which allow linearized controllability. Once such
loops are available, it is possible to employ standard Newton or
steepest descent methods. The theoretical justification of the
approach relies on results on genericity of nonsingular controls as
well as a simple convergence lemma.}
}
@INPROCEEDINGS{93cdc-sus-yang,
AUTHOR = {H.J. Sussmann and E.D. Sontag and Y. Yang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993},
TITLE = {A general result on the stabilization of linear systems
using bounded controls},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1802--1807},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs}
}
@INPROCEEDINGS{f8-conf,
AUTHOR = {Y. Yang and E.D. Sontag},
BOOKTITLE = {Proc. 1993 IEEE Conf. on Aerospace Control Systems, Thousand Oaks, CA, May 1993},
TITLE = {Stabilization with saturated actuators, a worked
example: F-8 longitudinal flight control},
YEAR = {1993},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {289--293},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs, aircraft, airplanes},
PDF = {../../FTPDIR/f8.pdf},
ABSTRACT = { This paper develops in detail an explicit design for
control under saturation limits for the linearized equations of
longitudinal flight control for an F-8 aircraft, and tests the
obtained controller on the original nonlinear model. }
}
@ARTICLE{two-layer,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Neural Networks},
TITLE = {Feedback stabilization using two-hidden-layer nets},
YEAR = {1992},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {981--990},
VOLUME = {3},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, feedback stabilization},
PDF = {../../FTPDIR/1982_sontag_feedback_stabilization_two_hidden_layers_ieee_tnn.pdf},
ABSTRACT = { This paper compares the representational capabilities
of one hidden layer and two hidden layer nets consisting of
feedforward interconnections of linear threshold units. It is
remarked that for certain problems two hidden layers are required,
contrary to what might be in principle expected from the known
approximation theorems. The differences are not based on numerical
accuracy or number of units needed, nor on capabilities for feature
extraction, but rather on a much more basic classification into
"direct" and "inverse" problems. The former correspond to the
approximation of continuous functions, while the latter are concerned
with approximating one-sided inverses of continuous functions - and
are often encountered in the context of inverse kinematics
determination or in control questions. A general result is given
showing that nonlinear control systems can be stabilized using two
hidden layers, but not in general using just one. }
}
@ARTICLE{MR1170916,
AUTHOR = {E.D. Sontag},
JOURNAL = {J. Comput. System Sci.},
TITLE = {Feedforward nets for interpolation and classification},
YEAR = {1992},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {20--48},
VOLUME = {45},
ADDRESS = {Orlando, FL, USA},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, VC dimension, boolean systems},
PUBLISHER = {Academic Press, Inc.},
PDF = {../../FTPDIR/jcss-sigmoids.pdf},
ABSTRACT = { This paper deals with single-hidden-layer feedforward
nets, studying various aspects of classification power and
interpolation capability. In particular, a worst-case analysis shows
that direct input to output connections in threshold nets double the
recognition but not the interpolation power, while using sigmoids
rather than thresholds allows doubling both. For other measures of
classification, including the Vapnik-Chervonenkis dimension, the
effect of direct connections or sigmoidal activations is studied in
the special case of two-dimensional inputs. },
DOI = {http://dx.doi.org/10.1016/0022-0000(92)90039-L}
}
@ARTICLE{MR1180510,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Universal nonsingular controls},
YEAR = {1992},
OPTMONTH = {},
NOTE = {Erratum appeared in SCL 20(1993), p. 77, can be found in same file.},
NUMBER = {3},
PAGES = {221--224},
VOLUME = {19},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {controllability, real-analytic functions},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/univctr.pdf},
ABSTRACT = { For analytic systems satisfying the strong
accessibility rank condition, generic inputs produce trajectories
along which the linearized system is controllable. Applications to
the steering of systems without drift are briefly mentioned. },
DOI = {http://dx.doi.org/10.1016/0167-6911(92)90116-A}
}
@ARTICLE{MR1178655,
AUTHOR = {Y. Wang and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Algebraic differential equations and rational control
systems},
YEAR = {1992},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {1126--1149},
VOLUME = {30},
KEYWORDS = {identifiability, observability, realization theory,
input/output system representations},
PDF = {../../FTPDIR/siam_rational_wang_sontag_reprint_siam1992.pdf},
ABSTRACT = { It is shown that realizability of an input/output
operators by a finite-dimensional continuous-time rational control
system is equivalent to the existence of a high-order algebraic
differential equation satisfied by the corresponding input/output
pairs ("behavior"). This generalizes, to nonlinear systems, the
classical equivalence between autoregressive representations and
finite dimensional linear realizability. }
}
@ARTICLE{MR1164098,
AUTHOR = {Y. Wang and E.D. Sontag},
JOURNAL = {Forum Math.},
TITLE = {Generating series and nonlinear systems: analytic
aspects, local realizability, and i/o representations},
YEAR = {1992},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {299--322},
VOLUME = {4},
KEYWORDS = {identifiability, observability, realization theory,
input/output system representations, real-analytic functions},
PDF = {../../FTPDIR/yw2.pdf},
ABSTRACT = { This paper studies fundamental analytic properties of
generating series for nonlinear control systems, and of the operators
they define. It then applies the results obtained to the extension of
facts, which relate realizability and algebraic input/output
equations, to local realizability and analytic equations. }
}
@INPROCEEDINGS{92cdc-fa,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992},
TITLE = {For neural networks, function determines form},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {26--31},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks}
}
@INPROCEEDINGS{dahleh-92acc,
AUTHOR = {M.A. Dahleh and E.D. Sontag and D.N.C. Tse and
J.N. Tsitsiklis},
BOOKTITLE = {Proc. Amer. Automatic Control Conf., Chicago, June 1992},
TITLE = {Worst-case identification of nonlinear fading memory
systems},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {241--245},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {information-based complexity, fading-memory systems,
stability, system identification, structured uncertainty},
PDF = {../../FTPDIR/ibc-fading-mem_acc1992.pdf},
ABSTRACT = {Preliminary version of paper published in Automatica in
1995.}
}
@INPROCEEDINGS{92ciss,
AUTHOR = {Y. Lin and E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, Princeton University, March 1992},
TITLE = {Gradient techniques for steering systems with no drift},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1003--1008},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{92acc,
AUTHOR = {R. Schwarzschild and E.D. Sontag and M.L.J. Hautus},
BOOKTITLE = {Proc. Amer. Automatic Control Conf. , Chicago, June 1992},
TITLE = {Output-Saturated Systems},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {2504--2509},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{130432,
AUTHOR = {H.T. Siegelmann and E.D. Sontag},
BOOKTITLE = {COLT '92: Proceedings of the fifth annual workshop on Computational learning theory},
TITLE = {On the computational power of neural nets},
YEAR = {1992},
ADDRESS = {New York, NY, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {440--449},
PUBLISHER = {ACM Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity,
super-Turing computation, recurrent neural networks},
DOI = {http://doi.acm.org/10.1145/130385.130432}
}
@INPROCEEDINGS{92cdc-wong,
AUTHOR = {H.T. Siegelmann and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992},
TITLE = {Some results on computing with neural nets},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1476--1481},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
analog computing, neural networks, computational complexity,
super-Turing computation, recurrent neural networks}
}
@INPROCEEDINGS{659746,
AUTHOR = {H.T. Siegelmann and E.D. Sontag and C.L. Giles},
BOOKTITLE = {Proceedings of the IFIP 12th World Computer Congress on Algorithms, Software, Architecture - Information Processing '92, Volume 1},
TITLE = {The Complexity of Language Recognition by Neural
Networks},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {329--335},
PUBLISHER = {North-Holland},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, computational complexity, machine learning,
recurrent neural networks, theory of computing and complexity}
}
@INPROCEEDINGS{92yale,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Seventh Yale Workshop on Adaptive and Learning Systems, Yale University, 1992},
TITLE = {Neural nets as systems models and controllers},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {73--79},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks, neural networks},
PDF = {../../FTPDIR/yale.pdf},
ABSTRACT = { A conference paper. Placed here because it was
requested, but contains little that is not also contained in the
survey on neural nets mentioned above. }
}
@INPROCEEDINGS{92nolcos-es,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993},
TITLE = {Systems combining linearity and saturations, and
relations to neural nets},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {(Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992, M. Fliess, Ed., IFAC Publications, pp. 242-247)},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {15--21},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, recurrent neural networks}
}
@INPROCEEDINGS{92nolcos-yuandan,
AUTHOR = {E.D. Sontag and Y. Lin},
BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, M. Fliess Ed., Pergamon Press, Oxford, 1993},
TITLE = {Stabilization with respect to noncompact sets: Lyapunov
characterizations and effect of bounded inputs},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 9--14},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {43--49},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs},
PDF = {../../FTPDIR/92nolcos-yl.pdf}
}
@INPROCEEDINGS{92cdc-yw,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992},
TITLE = {I/O equations in discrete and continuous time},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3661--3662},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identifiability, observability, realization theory}
}
@INPROCEEDINGS{92nolcos-yss,
AUTHOR = {Y. Yang and H.J. Sussmann and E.D. Sontag},
BOOKTITLE = {Nonlinear Control Systems Design 1992, IFAC Symposia Series, 1993, M. Fliess Ed., Pergamon Press, Oxford, 1993},
TITLE = {Stabilization of linear systems with bounded controls},
YEAR = {1992},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Also in Proc. Nonlinear Control Systems Design Symp., Bordeaux, June 1992,(M. Fliess, Ed.), IFAC Publications, pp. 15-20.},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {51--56},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs}
}
@INCOLLECTION{MR1131981,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Analysis of controlled dynamical systems (Lyon, 1990)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Transitivity and forward accessibility of discrete-time
nonlinear systems},
YEAR = {1991},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {21--34},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {8}
}
@INCOLLECTION{MR1114761,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Neural networks (New Brunswick, NJ, 1990)},
PUBLISHER = {Academic Press},
TITLE = {Capabilities and training of feedforward nets},
YEAR = {1991},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {303--321},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/90caip.pdf},
ABSTRACT = { This paper surveys recent work by the author on
learning and representational capabilities of feedforward nets. The
learning results show that, among two possible variants of the
so-called backpropagation training method for sigmoidal nets, both of
which variants are used in practice, one is a better generalization
of the older perceptron training algorithm than the other. The
representation results show that nets consisting of sigmoidal neurons
have at least twice the representational capabilities of nets that
use classical threshold neurons, at least when this increase is
quantified in terms of classification power. On the other hand,
threshold nets are shown to be more useful when approximating
implicit functions, as illustrated with an application to a typical
control problem. }
}
@INCOLLECTION{MR1125161,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {New trends in systems theory (Genoa, 1990)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Input/output and state-space stability},
YEAR = {1991},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {684--691},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {7},
KEYWORDS = {input to state stability, input to state stability},
PDF = {../../FTPDIR/90genoa.pdf},
ABSTRACT = { This conference paper reviews various results relating
state-space (Lyapunov) stabilization and exponential stabilization to
several notions of input/output or bounded-input bounded-output
stabilization. It also provides generalizations of some of these
results to systems with saturating controls. Some of these latter
results were not included in journal papers. }
}
@INCOLLECTION{MR1296059,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Mathematical system theory},
PUBLISHER = {Springer},
TITLE = {Kalman's controllability rank condition: from linear to
nonlinear},
YEAR = {1991},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {453--462},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {controllability},
PDF = {../../FTPDIR/rek-volume.pdf},
ABSTRACT = { The notion of controllability was identified by Kalman
as one of the central properties determining system behavior. His
simple rank condition is ubiquitous in linear systems analysis. This
article presents an elementary and expository overview of the
generalizations of this test to a condition for testing accessibility
of discrete and continuous time nonlinear systems. }
}
@ARTICLE{MR1112756,
AUTHOR = {Y. Lin and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A universal formula for stabilization with bounded
controls},
YEAR = {1991},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {393--397},
VOLUME = {16},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {stabilization, nonlinear systems, saturation,
bounded inputs, control-Lyapunov functions, real-analytic functions},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/boundedart.pdf},
ABSTRACT = { We provide a formula for a stabilizing feedback law
using a bounded control, under the assumption that an appropriate
control-Lyapunov function is known. Such a feedback, smooth away from
the origin and continuous everywhere, is known to exist via
Artstein's Theorem. As in the unbounded-control case treated in a
previous note, we provide an explicit and ``universal'' formula given
by an algebraic function of Lie derivatives. In particular, we extend
to the bounded case the result that the feedback can be chosen
analytic if the Lyapunov function and the vector fields defining the
system are analytic. },
DOI = {http://dx.doi.org/10.1016/0167-6911(91)90111-Q}
}
@ARTICLE{MR1136617,
AUTHOR = {H. T. Siegelmann and E.D. Sontag},
JOURNAL = {Applied Mathematics Letters},
TITLE = {Turing computability with neural nets},
YEAR = {1991},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {6},
PAGES = {77--80},
VOLUME = {4},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, computational complexity, recurrent neural networks},
PDF = {../../FTPDIR/aml-turing.pdf},
ABSTRACT = { This paper shows the existence of a finite neural
network, made up of sigmoidal neurons, which simulates a universal
Turing machine. It is composed of less than 100,000 synchronously
evolving processors, interconnected linearly. High-order connections
are not required. (Note: this paper was placed here by special
request. The results in this paper have been by now improved
considerably: see the JCSS pape which among other aspects provides a
polynomial time simulation. This paper, based on a unary encoding,
results in an exponential slowdown). }
}
@ARTICLE{109699,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
JOURNAL = {Neural Networks},
TITLE = {Back propagation separates where perceptrons do},
YEAR = {1991},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {243--249},
VOLUME = {4},
ADDRESS = {Oxford, UK, UK},
KEYWORDS = {machine learning, artificial intelligence,
gradient dynamics, gradient descent, gradient systems,
gradient descent, numerical methods, dynamics of algorithms,
neural networks},
PUBLISHER = {Elsevier Science Ltd.},
PDF = {../../FTPDIR/converge-nn.pdf},
ABSTRACT = { Feedforward nets with sigmoidal activation functions
are often designed by minimizing a cost criterion. It has been
pointed out before that this technique may be outperformed by the
classical perceptron learning rule, at least on some problems. In
this paper, we show that no such pathologies can arise if the error
criterion is of a threshold LMS type, i.e., is zero for values
``beyond'' the desired target values. More precisely, we show that if
the data are linearly separable, and one considers nets with no
hidden neurons, then an error function as above cannot have any local
minima that are not global. In addition, the proof gives the
following stronger result, under the stated hypotheses: the
continuous gradient adjustment procedure is such that from any
initial weight configuration a separating set of weights is obtained
in finite time. This is a precise analogue of the Perceptron Learning
Theorem. The results are then compared with the more classical
pattern recognition problem of threshold LMS with linear activations,
where no spurious local minima exist even for nonseparable data: here
it is shown that even if using the threshold criterion, such bad
local minima may occur, if the data are not separable and sigmoids
are used. keywords = { neural networks , feedforward neural nets }, },
DOI = {http://dx.doi.org/10.1016/0893-6080(91)90008-S}
}
@INPROCEEDINGS{91ciss-francesca,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991},
TITLE = {Accessibility of discrete-time nonlinear systems, and
some relations to chaotic dynamics},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {731--736},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{91ecc,
AUTHOR = {F. Albertini and E.D. Sontag},
BOOKTITLE = {Proc. European Control Conf. , Vol 1, Grenoble, July 1991},
TITLE = {Some connections between chaotic dynamical systems and
control systems},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {58--163},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {chaotic systems, controllability},
PDF = {../../FTPDIR/91ecc.pdf},
ABSTRACT = { This paper shows how to extend recent results of
Colonius and Kliemann, regarding connections between chaos and
controllability, from continuous to discrete time. The extension is
nontrivial because the results all rely on basic properties of the
accessibility Lie algebra which fail to hold in discrete time. Thus,
this paper first develops further results in nonlinear accessibility,
and then shows how a theorem can be proved, which while analogous to
the one given in the work by Colonius and Klieman, also exhibits some
important differences. A counterexample is used to show that the
theorem given in continuous time cannot be generalized in a
straightforward manner. }
}
@INPROCEEDINGS{91ciss-yuandan,
AUTHOR = {Y. Lin and E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991},
TITLE = {Further universal formulas for Lyapunov approaches to
nonlinear stabilization},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {541--546},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{123410,
AUTHOR = {W. Maass and G. Schnitger and E.D. Sontag},
BOOKTITLE = {Proceedings of the 32nd annual symposium on Foundations of computer science},
TITLE = {On the computational power of sigmoid versus Boolean
threshold circuits (extended abstract)},
YEAR = {1991},
ADDRESS = {Los Alamitos, CA, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {767--776},
PUBLISHER = {IEEE Computer Society Press},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, theory of computing and complexity}
}
@INPROCEEDINGS{91acc-renee,
AUTHOR = {R. Schwarzschild and E.D. Sontag},
BOOKTITLE = {Proc. Amer. Automatic Control Conf., Boston, June 1991},
TITLE = {Algebraic theory of sign-linear systems},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {799--804},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{91ciss-renee,
AUTHOR = {R. Schwarzschild and E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991},
TITLE = {Quantized systems, saturated measurements, and
sign-linear systems},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {134--139},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {observability, saturation}
}
@INPROCEEDINGS{91ciss-twolayer,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins University, March 1991},
TITLE = {Capabilities of four- vs three-layer nets, and control
applications},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {558--563},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{91acc-twolayer,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Amer. Automatic Control Conf. , Boston, June 1991},
TITLE = {Feedback Stabilization Using Two-Hidden-Layer Nets},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {815--820},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{91cdc-wang,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, 1991},
TITLE = {I/O equations for nonlinear systems and observation
spaces},
YEAR = {1991},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {720--725},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identifiability, observability, realization theory,
real-analytic functions},
PDF = {../../FTPDIR/91cdc-ywang.pdf},
ABSTRACT = {This paper studies various types of input/output
representations for nonlinear continuous time systems. The algebraic
and analytic i/o equations studied in previous papers by the authors
are generalized to integral and integro-differential equations, and
an abstract notion is also considered. New results are given on
generic observability, and these results are then applied to give
conditions under which that the minimal order of an equation equals
the minimal possible dimension of a realization, just as with linear
systems but in contrast to the discrete time nonlinear theory. }
}
@BOOK{MR1070569,
PUBLISHER = {Springer-Verlag},
TITLE = {Mathematical Control Theory. Deterministic
Finite-Dimensional Systems},
YEAR = {1990},
AUTHOR = {E.D. Sontag},
ALTEDITOR = {},
ADDRESS = {New York},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
SERIES = {Texts in Applied Mathematics},
VOLUME = {6},
PAGES = {xiv+396},
ABSTRACT = { The second edition (1998) is now online; please follow
that link. }
}
@INCOLLECTION{MR1206692,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Control of uncertain systems (Bremen, 1989)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Constant McMillan degree and the continuous
stabilization of families of transfer matrices},
YEAR = {1990},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {289--295},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {6},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/constant_mcmillan_degree_continuous_stabilization_springer1990.pdf}
}
@INCOLLECTION{MR1115377,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Robust control of linear systems and nonlinear control (Amsterdam, 1989)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Feedback stabilization of nonlinear systems},
YEAR = {1990},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {61--81},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {4},
PDF = {../../FTPDIR/89mtns-feed.pdf},
ABSTRACT = { This paper surveys some well-known facts as well as
some recent developments on the topic of stabilization of nonlinear
systems. (NOTE: figures are not included in file; they were
pasted-in.) }
}
@INCOLLECTION{MR1061384,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Nonlinear controllability and optimal control},
PUBLISHER = {Dekker},
TITLE = {Integrability of certain distributions associated with
actions on manifolds and applications to control problems},
YEAR = {1990},
ADDRESS = {New York},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {81--131},
SERIES = {Monogr. Textbooks Pure Appl. Math.},
OPTTYPE = {},
VOLUME = {133},
KEYWORDS = {controllability},
PDF = {../../FTPDIR/actions-report.pdf},
ABSTRACT = { Results are given on the integrability of certain
distributions which arise from smoothly parametrized families of
diffeomorphisms acting on manifolds. Applications to control problems
and in particular to the problem of sampling are discussed. Pages
42-50 apply the results to the control of continuous time systems;
this is an exposition of some of the basic results of the Lie
algebraic accessibility theory. }
}
@INCOLLECTION{MR1115322,
AUTHOR = {E.D. Sontag and Y. Wang},
BOOKTITLE = {Realization and modelling in system theory (Amsterdam, 1989)},
PUBLISHER = {Birkhuser Boston},
TITLE = {Input/output equations and realizability},
YEAR = {1990},
ADDRESS = {Boston, MA},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {125--132},
SERIES = {Progr. Systems Control Theory},
OPTTYPE = {},
VOLUME = {3},
KEYWORDS = {identifiability, observability, realization theory},
PDF = {../../FTPDIR/89mtns-yw_recompile_2015.pdf}
}
@ARTICLE{Jakubczyk_sicopt90,
AUTHOR = {B. Jakubczyk and E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Controllability of nonlinear discrete-time systems: a
Lie-algebraic approach},
YEAR = {1990},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {1--33},
VOLUME = {28},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {discrete-time},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/dt-controllability_jakubcyk_sontag_reprint_siam1990.pdf},
ABSTRACT = { This paper presents a geometric study of
controllability for discrete-time nonlinear systems. Various
accessibility properties are characterized in terms of Lie algebras
of vector fields. Some of the results obtained are parallel to
analogous ones in continuous-time, but in many respects the theory is
substantially different and many new phenomena appear. },
DOI = {http://dx.doi.org/10.1137/0328001}
}
@ARTICLE{MR1048003,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Further facts about input to state stabilization},
YEAR = {1990},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {473--476},
VOLUME = {35},
KEYWORDS = {input to state stability, ISS, stabilization},
PDF = {../../FTPDIR/further-iss90_reprint.pdf},
ABSTRACT = { Previous results about input to state stabilizability
are shown to hold even for systems which are not linear in controls,
provided that a more general type of feedback be allowed.
Applications to certain stabilization problems and coprime
factorizations, as well as comparisons to other results on input to
state stability, are also briefly discussed.d local minima may occur,
if the data are not separable and sigmoids are used. }
}
@ARTICLE{MR1067673,
AUTHOR = {E.D. Sontag and Y. Wang},
JOURNAL = {Linear Algebra Appl.},
TITLE = {Pole shifting for families of linear systems depending
on at most three parameters},
YEAR = {1990},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {3--38},
VOLUME = {137/138},
KEYWORDS = {systems over rings, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/quaternions.pdf},
ABSTRACT = { We prove that for any family of n-dimensional
controllable linear systems, continuously parameterized by up to
three parameters, and for any continuous selection of n eigenvalues
(in complex conjugate pairs), there is some dynamic controller of
dimension 3n which is itself continuously parameterized and for which
the closed-loop eigenvalues are these same eigenvalues, each counted
4 times. An analogous result holds also for smooth parameterizations. }
}
@INPROCEEDINGS{Souvaine,
AUTHOR = {T. Asano and J. Hershberger and J. Pach and E.D. Sontag and
D. Souivaine and S. Suri},
BOOKTITLE = {Proceedings of the Second Canadian Conf. on Computational Geometry, Ottawa, Canada, 1990},
TITLE = {Separating bi-chromatic points by parallel lines},
YEAR = {1990},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {46--49},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {computational geometry},
PDF = {../../FTPDIR/dls.pdf},
ABSTRACT = { Given a 2-coloring of the vertices of a regular n-gon
P, how many parallel lines are needed to separate the vertices into
monochromatic subsets? We prove that floor(n/2) is a tight upper
bound, and also provide an O(n log n) time algorithm to determine the
direction that gives the minimum number of lines. If the polygon is a
non-regular convex polygon, then n-3 lines may be necessary, while
n-2 lines always suffice. This problem arises in machine learning and
has implications about the representational capabilities of some
neural networks. }
}
@INPROCEEDINGS{dewan,
AUTHOR = {H. Dewan and E.D. Sontag},
BOOKTITLE = {Proc. Int. Joint Conf. on Neural Networks, Washington, DC, Jan. 1990, Lawrence Erlbaum Associates, Inc., Publishers, ISBN 0-8058-0775-6},
TITLE = {Extrapolatory methods for speeding up the BP algorithm},
YEAR = {1990},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {I.613--616},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/1990_dewan_sontag_extrapolatory_neural.pdf},
ABSTRACT = {We describe a speedup technique that uses extrapolatory
methods to predict the weights in a Neural Network using Back
Propagation (BP) learning. The method is based on empirical
observations of the way the weights change as a function of time. We
use numerical function fitting techniques to determine the parameters
of an extrapolation function and then use this function to project
weights into the future. Significant computational savings result by
using the extrapolated weights to jump over many iterations of the
standard algorithm, achieving comparable performance with fewer
iterations.}
}
@INPROCEEDINGS{90ciss,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Info. Sci. and Systems, Princeton, 1990},
TITLE = {Comparing sigmoids and heavisides},
YEAR = {1990},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {654--659},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, boolean systems}
}
@INPROCEEDINGS{119971,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {NIPS-3: Proceedings of the 1990 conference on Advances in neural information processing systems 3},
TITLE = {Remarks on interpolation and recognition using neural
nets},
YEAR = {1990},
ADDRESS = {San Francisco, CA, USA},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
NOTE = {Proc. NIPS(NeurIPS)-3, Denver, 1990, https://papers.nips.cc/paper_files/paper/1990},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {939--945},
PUBLISHER = {Morgan Kaufmann Publishers Inc.},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {NeurIPS, machine learning, artificial intelligence,
neural networks}
}
@INPROCEEDINGS{90cdc,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Honolulu, Dec. 1990, IEEE Publications, 1990},
TITLE = {Nonlinear output feedback design for linear systems with
saturating controls},
YEAR = {1990},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {3414--3416},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {saturation, bounded inputs},
PDF = {../../FTPDIR/90cdc.pdf},
ABSTRACT = { This paper shows the existence of (nonlinear) smooth
dynamic feedback stabilizers for linear time invariant systems under
input constraints, assuming only that open-loop asymptotic
controllability and detectability hold. }
}
@INPROCEEDINGS{90IFAC,
AUTHOR = {Y. Wang and E.D. Sontag},
BOOKTITLE = {Proc. 11th IFAC World Congress, Tallinn, former USSR, 1990},
TITLE = {Realization of families of generating series:
differential algebraic and state space equations},
YEAR = {1990},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {62--66},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identifiability, observability, realization theory}
}
@TECHREPORT{SYCON-90-13,
AUTHOR = {F. Albertini and E.D. Sontag},
INSTITUTION = {Rutgers Center for Systems and Control},
TITLE = {Some connections between chaotic dynamical systems and
control systems},
YEAR = {1990},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {SYCON-90-13},
OPTTYPE = {}
}
@INCOLLECTION{MR1013210,
AUTHOR = {B. Jakubczyk and E.D. Sontag},
BOOKTITLE = {Modern optimal control},
PUBLISHER = {Dekker},
TITLE = {Nonlinear discrete-time systems. Accessibility
conditions},
YEAR = {1989},
ADDRESS = {New York},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {173--185},
SERIES = {Lecture Notes in Pure and Appl. Math.},
OPTTYPE = {},
VOLUME = {119},
PDF = {../jakubczyk_sontag_nonlinear_discrete_time_systems_book_1989_from_gbooks.pdf}
}
@ARTICLE{MR1029482,
AUTHOR = {A. Arapostathis and B. Jakubczyk and H.-G. Lee and
S. I. Marcus and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {The effect of sampling on linear equivalence and
feedback linearization},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {373--381},
VOLUME = {13},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {discrete-time, sampled-data systems,
discrete-time systems, sampling},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/gri.pdf},
ABSTRACT = { We investigate the effect of sampling on linearization
for continuous time systems. It is shown that the discretized system
is linearizable by state coordinate change for an open set of
sampling times if and only if the continuous time system is
linearizable by state coordinate change. Also, it is shown that
linearizability via digital feedback imposes highly nongeneric
constraints on the structure of the plant, even if this is known to
be linearizable with continuous-time feedback. },
DOI = {http://dx.doi.org/10.1016/0167-6911(89)90103-5}
}
@ARTICLE{MR1014237,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A ``universal'' construction of Artstein's theorem on
nonlinear stabilization},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {117--123},
VOLUME = {13},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {control-Lyapunov functions, stabilization,
real-analytic functions},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/art-sycon8903.pdf},
ABSTRACT = { This note presents an explicit proof of the theorem -
due to Artstein - which states that the existence of a smooth
control-Lyapunov function implies smooth stabilizability. Moreover,
the result is extended to the real-analytic and rational cases as
well. The proof uses a "universal" formula given by an algebraic
function of Lie derivatives; this formula originates in the solution
of a simple Riccati equation. }
}
@ARTICLE{sigmoids-nc,
AUTHOR = {E.D. Sontag},
JOURNAL = {Neural Computation},
TITLE = {Sigmoids distinguish more efficiently than Heavisides},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {470--472},
VOLUME = {1},
KEYWORDS = {machine learning, artificial intelligence,
neural networks, boolean systems},
PDF = {../../FTPDIR/sigmoids_efficient_sontag_neural_comp1989.pdf},
ABSTRACT = {Every dichotomy on a 2k-point set in Rn can be
implemented by a neural net with a single hidden layer containing k
sigmoidal neurons. If the neurons were of a hardlimiter (Heaviside)
type, 2k-1 would be in general needed.}
}
@ARTICLE{ISS89,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Smooth stabilization implies coprime factorization},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {435--443},
VOLUME = {34},
KEYWORDS = {input to state stability, ISS, input to state stability},
PDF = {../../FTPDIR/coprime-factorizations.pdf},
ABSTRACT = { This paper shows that coprime right factorizations
exist for the input to state mapping of a continuous time nonlinear
system provided that the smooth feedback stabilization problem be
solvable for this system. In particular, it follows that feedback
linearizable systems admit such factorizations. In order to establish
the result a Lyapunov-theoretic definition is proposed for bounded
input bounded output stability. The main technical fact proved
relates the notion of stabilizability studied in the state space
nonlinear control literature to a notion of stability under bounded
control perturbations analogous to those studied in operator
theoretic approaches to systems; it states that smooth stabilization
implies smooth input-to-state stabilization. (Note: This is the
original ISS paper, but the ISS results have been much improved in
later papers. The material on coprime factorizations is still of
interest, but the 89 CDC paper has some improvements and should be
read too.) }
}
@ARTICLE{MR1102346,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
JOURNAL = {Complex Systems},
TITLE = {Backpropagation can give rise to spurious local minima
even for networks without hidden layers},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {91--106},
VOLUME = {3},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/complex_systems.pdf},
ABSTRACT = { We give an example of a neural net without hidden
layers and with a sigmoid transfer function, together with a training
set of binary vectors, for which the sum of the squared errors,
regarded as a function of the weights, has a local minimum which is
not a global minimum. The example consists of a set of 125 training
instances, with four weights and a threshold to be learnt. We do not
know if substantially smaller binary examples exist. }
}
@ARTICLE{MR993944,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
JOURNAL = {Systems Control Lett.},
TITLE = {Further comments on the stabilizability of the angular
velocity of a rigid body},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {213--217},
VOLUME = {12},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {satellite control, feedback stabilization},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/satel.pdf},
ABSTRACT = { We prove that the angular velocity equations can be
smoothly stabilized with a single torque controller for bodies having
an axis of symmetry. This complements a recent result of Aeyels and
Szafranski. },
DOI = {http://dx.doi.org/10.1016/0167-6911(89)90052-2}
}
@ARTICLE{MR1006847,
AUTHOR = {E.D. Sontag and Y. Yamamoto},
JOURNAL = {Systems Control Lett.},
TITLE = {On the existence of approximately coprime factorizations
for retarded systems},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {53--58},
VOLUME = {13},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {delay-differential systems},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/yy-coprime.pdf},
ABSTRACT = { This note establishes a result linking algebraically
coprime factorizations of transfer matrices of delay systems to
approximately coprime factorizations in the sense of distributions.
The latter have been employed by the second author in the study of
function-space controllability for such systems. },
DOI = {http://dx.doi.org/10.1016/0167-6911(89)90020-0}
}
@ARTICLE{MR1025981,
AUTHOR = {Y. Wang and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {On two definitions of observation spaces},
YEAR = {1989},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {279--289},
VOLUME = {13},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {observability, identifiability, observables,
observation space, realization theory},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/yw-obs.pdf},
ABSTRACT = { This paper establishes the equality of the observation
spaces defined by means of piecewise constant controls with those
defined in terms of differentiable controls. },
DOI = {http://dx.doi.org/10.1016/0167-6911(89)90116-3}
}
@INPROCEEDINGS{MR1039005,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)},
TITLE = {Remarks on stabilization and input-to-state stability},
YEAR = {1989},
ADDRESS = {New York},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1376--1378},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, ISS, stabilization},
PDF = {../../FTPDIR/89cdc-stab-reprint.pdf},
ABSTRACT = { This paper describes how notions of input-to-state
stabilization are useful when stabilizing cascades of systems. The
simplest result along these lines is local, and it states that a
cascade of two locally asymptotically stable systems is again
asystable. A global result is obtained if both systems have the
origin as a globally asymptotically stable state and the "converging
input bounded state" property holds for the second system. Relations
to input to state stability and the "bounded input bounded state"
property as mentioned as well. }
}
@INPROCEEDINGS{MR1038933,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)},
TITLE = {Remarks on the time-optimal control of a class of
Hamiltonian systems},
YEAR = {1989},
ADDRESS = {New York},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {217--221},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {robotics, optimal control},
PDF = {../../FTPDIR/89cdc-ham.pdf},
ABSTRACT = { This paper introduces a subclass of Hamiltonian control
systems motivated by mechanical models. It deals with time-optimal
control problems. The main results characterize regions of the state
space where singular trajectories cannot exist, and provide
high-order conditions for optimality. }
}
@INPROCEEDINGS{MR1038986,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)},
TITLE = {Some connections between stabilization and factorization},
YEAR = {1989},
ADDRESS = {New York},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {990--995},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/89cdccopr-reformat.pdf},
ABSTRACT = { Coprime right fraction representations are obtained for
nonlinear systems defined by differential equations, under
assumptions of stabilizability and detectability. A result is also
given on left (not necessarily coprime) factorizations. }
}
@INPROCEEDINGS{feedback-CISS89,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989},
TITLE = {Some recent results on nonlinear feedback},
YEAR = {1989},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {151--156},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{SYCON12,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Int. Conf. Neural Networks, Washington, DC, June 1989},
TITLE = {Backpropagation Separates when Perceptrons Do},
YEAR = {1989},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {639--642},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/89ICNN.pdf}
}
@INPROCEEDINGS{neural-CISS89,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989},
TITLE = {Remarks on local minima in backpropagation},
YEAR = {1989},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {432--435},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks}
}
@INPROCEEDINGS{YW-CISS,
AUTHOR = {Y. Wang and E.D. Sontag},
BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989},
TITLE = {A new result on the relation between
differential-algebraic realizability and state space realizations},
YEAR = {1989},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {143--147},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {observables, observation space, identifiability,
observability, realization theory}
}
@INPROCEEDINGS{MR1039048,
AUTHOR = {Y. Wang and E.D. Sontag},
BOOKTITLE = {Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989)},
TITLE = {Realization and input/output relations: the analytic
case},
YEAR = {1989},
ADDRESS = {New York},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1975--1980},
PUBLISHER = {IEEE},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {identifiability, observability, realization theory,
real-analytic functions}
}
@TECHREPORT{SYCON-89-12,
AUTHOR = {E.D. Sontag},
INSTITUTION = {Rutgers Center for Systems and Control},
TITLE = {Sigmoids distinguish more efficiently than Heavisides},
YEAR = {1989},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {SYCON-89-12},
OPTTYPE = {},
KEYWORDS = {machine learning, neural networks}
}
@BOOK{siam88book,
PUBLISHER = {SIAM},
TITLE = {Linear Algebra in Signals, Systems, and Control (edited
book)},
YEAR = {1988},
AUTHOR = {B.N. Datta and C.R. Johnson and M.A. Kaashoek and
R.J. Plemmons and E.D. Sontag},
ALTEDITOR = {},
OPTADDRESS = {},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{CHOW,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Analysis and Control of Nonlinear Systems},
PUBLISHER = {North Holland, Amsterdam},
TITLE = {A Chow property for sampled bilinear systems},
YEAR = {1988},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C.I. Byrnes and C.F. Martin and R. Saeks},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {205--211},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {discrete-time, bilinear systems},
PDF = {../../FTPDIR/bilin2.pdf},
ABSTRACT = { This paper studies accessibility (weak controllability)
of bilinear systems under constant sampling rates. It is shown that
the property is preserved provided that the sampling period satisfies
a condition related to the eigenvalues of the autonomous dynamics
matrix. This condition generalizes the classical Kalman-Ho-Narendra
criterion which is well known in the linear case, and which, for
observability, results in the classical Nyquist theorem. }
}
@INCOLLECTION{EQUI-MTNS87,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Analysis and Control of Nonlinear Systems},
PUBLISHER = {North Holland, Amsterdam},
TITLE = {An explicit construction of the equilinearization
controller},
YEAR = {1988},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {C.I. Byrnes and C.F. Martin and R. Saek},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {483--492},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/87mtnslin.pdf},
ABSTRACT = { This paper provides further results about the
equilinearization method of control design recently introduced by the
author. A simplified derivation of the controller is provided, as
well as a theorem on local stabilization along reference
trajectories. }
}
@ARTICLE{MR960665,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Bilinear realizability is equivalent to existence of a
singular affine differential I/O equation},
YEAR = {1988},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {181--187},
VOLUME = {11},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {identification, identifiability, observability,
observation space, real-analytic functions},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/bilinrealiz.pdf},
ABSTRACT = { For continuous time analytic input/output maps, the
existence of a singular differential equation relating derivatives of
controls and outputs is shown to be equivalent to bilinear
realizability. A similar result holds for the problem of immersion
into bilinear systems. The proof is very analogous to that of the
corresponding, and previously known, result for discrete time. },
DOI = {http://dx.doi.org/10.1016/0167-6911(88)90057-6}
}
@ARTICLE{MR957656,
AUTHOR = {E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {Controllability is harder to decide than accessibility},
YEAR = {1988},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {1106--1118},
VOLUME = {26},
ADDRESS = {Philadelphia, PA, USA},
KEYWORDS = {computational complexity, controllability,
computational complexity},
PUBLISHER = {Society for Industrial and Applied Mathematics},
PDF = {../../FTPDIR/decide_controllability_sontag_reprint_siam1998.pdf},
ABSTRACT = { The present article compares the difficulties of
deciding controllability and accessibility. These are standard
properties of control systems, but complete algebraic
characterizations of controllability have proved elusive. We show in
particular that for subsystems of bilinear systems, accessibility can
be decided in polynomial time, but controllability is NP-hard. },
DOI = {http://dx.doi.org/10.1137/0326061}
}
@ARTICLE{MR929174,
AUTHOR = {E.D. Sontag},
JOURNAL = {Internat. J. Control},
TITLE = {Finite-dimensional open-loop control generators for
nonlinear systems},
YEAR = {1988},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {537--556},
VOLUME = {47},
PDF = {../../FTPDIR/fdg.pdf},
ABSTRACT = { This paper concerns itself with the existence of
open-loop control generators for nonlinear (continuous-time) systems.
The main result is that, under relatively mild assumptions on the
original system, and for each fixed compact subset of the state
space, there always exists one such generator. This is a new system
with the property that the controls it produces are sufficiently rich
to preserve complete controllability along nonsingular trajectories.
General results are also given on the continuity and
differentiability of the input to state mapping for various p-norms
on controls, as well as a comparison of various nonlinear
controllability notions. }
}
@INPROCEEDINGS{88cdc-dec,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988},
TITLE = {Some complexity questions regarding controllability},
YEAR = {1988},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1326--1329},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {theory of computing and complexity,
computational complexity, controllability, computational complexity},
PDF = {../../FTPDIR/88cdcdec.pdf},
ABSTRACT = { It has been known for a long time that certain
controllability properties are more difficult to verify than others.
This article makes this fact precise, comparing controllability with
accessibility, for a wide class of nonlinear continuous time systems.
The original contribution is in formalizing this comparison in the
context of computational complexity. (This paper placed here by
special request.) }
}
@INPROCEEDINGS{88cdc-copr,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Austin, Dec. 1988},
TITLE = {Stabilizability, i/o stability, and coprime
factorizations},
YEAR = {1988},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {457--458},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {input to state stability, coprime factorizations,
stabilization}
}
@TECHREPORT{SYCON4,
AUTHOR = {E.D. Sontag},
INSTITUTION = {Rutgers Center for Systems and Control},
TITLE = {Integrability of certain distributions associated to
actions on manifolds and an introduction to Lie-algebraic control},
YEAR = {1988},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {SYCON-88-04},
OPTTYPE = {}
}
@TECHREPORT{SYCON2,
AUTHOR = {E.D. Sontag},
INSTITUTION = {Rutgers Center for Systems and Control},
TITLE = {Some remarks on the backpropagation algorithm for neural
net learning},
YEAR = {1988},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {SYCON-88-02},
OPTTYPE = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/sycon88-02.pdf},
ABSTRACT = { This is a very old informal report that discusses the
study of local minima of quadratic loss functions for fitting errors
in sigmoidal neural net learning. It also includes several remarks
concerning the growth of weights during gradient descent. There is
nothing very interesting here - far better knowledge is now available
- but the report was placed here by request. }
}
@INCOLLECTION{ENCYC1,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Encycl. of Systems and Control},
PUBLISHER = {Pergamon Press},
TITLE = {Reachability, observability, and realization of a class
of discrete-time nonlinear systems},
YEAR = {1987},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {3288--3293},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {observability}
}
@ARTICLE{MR917700,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A remark on bilinear systems and moduli spaces of
instantons},
YEAR = {1987},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {361--367},
VOLUME = {9},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {bilinear systems, moduli spaces, instantons},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/instantons.pdf},
ABSTRACT = { Explicit equations are given for the moduli space of
framed instantons as a quasi-affine variety, based on the
representation theory of noncommutative power series, or
equivalently, the minimal realization theory of bilinear systems. },
DOI = {http://dx.doi.org/10.1016/0167-6911(87)90064-8}
}
@ARTICLE{MR907356,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Controllability and linearized regulation},
YEAR = {1987},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {10},
PAGES = {877--888},
VOLUME = {32},
PDF = {../../FTPDIR/lin.pdf},
ABSTRACT = { A nonlinear controllable plant, under mild technical
conditions, admits a precompensator with the following property:
along control trajectories joining pairs of states, the composite
system (precompensator plus plant) is, up to first order, isomorphic
to a parallel connection of integrators. }
}
@ARTICLE{BOSE,
AUTHOR = {E.D. Sontag},
JOURNAL = {Linear Alg. and Applications},
TITLE = {Review of Multidimensional Systems Theory},
YEAR = {1987},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {273--278},
VOLUME = {87},
PDF = {../../FTPDIR/bose.pdf},
ABSTRACT = { A book review which also provides a quick introduction
to questions of stability and positivity of multivariable polynomials
for 2D and spatially-distributed systems. }
}
@INPROCEEDINGS{GRI,
AUTHOR = {B. Jakubczyk and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987},
TITLE = {The effect of sampling on feedback linearization},
YEAR = {1987},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1374--1379},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{EQUI-CDC87,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Los Angeles, Dec.1987},
TITLE = {An approach to the automatic design of first-order
controllers along reference trajectories},
YEAR = {1987},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {363--1367},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{JHU87,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press},
TITLE = {Equilinearization: A simplified derivation and
experimental results},
YEAR = {1987},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {490--495},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@TECHREPORT{CAIP1,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
INSTITUTION = {Rutgers Center for Computer Aids for Industrial Productivity},
TITLE = {Optimization algorithms for image restoration and
segmentation},
YEAR = {1987},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {34},
OPTTYPE = {}
}
@INCOLLECTION{MR862338,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Algebraic and geometric methods in nonlinear control theory},
PUBLISHER = {Reidel},
TITLE = {Orbit theorems and sampling},
YEAR = {1986},
ADDRESS = {Dordrecht},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {441--483},
SERIES = {Math. Appl.},
OPTTYPE = {},
VOLUME = {29},
PDF = {../../FTPDIR/85paris.pdf},
ABSTRACT = { This paper proposes a notion of smooth action on a
manifold, and establishes a general integrability result for certain
associated distributions. As corollaries, various classical and new
results on manifold structures of orbits are established, and the
main theorem on preservation of transitivity under sampling is shown
to be a simple consequence. }
}
@ARTICLE{MR836650,
AUTHOR = {M. L. J. Hautus and E.D. Sontag},
JOURNAL = {J. Pure Appl. Algebra},
TITLE = {New results on pole-shifting for parametrized families
of systems},
YEAR = {1986},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {229--244},
VOLUME = {40},
KEYWORDS = {systems over rings, pole-shifting,
parametric classes of systems, real-analytic functions},
PDF = {../../FTPDIR/mh2.pdf},
ABSTRACT = { New results are given on the pole-shifting problem for
commutative rings, and these are then applied to conclude that rings
of continuous, smooth, or real-analytic functions on a manifold X are
PA rings if and only if X is one-dimensional. }
}
@ARTICLE{MR850445,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {An eigenvalue condition for sample weak controllability
of bilinear systems},
YEAR = {1986},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {313--315},
VOLUME = {7},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {discrete-time},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/bilin-scl.pdf},
ABSTRACT = { Weak controllability of bilinear systems is preserved
under sampling provided that the sampling period satisfies a
condition related to the eigenvalues of the autonomous dynamics
matrix. This condition generalizes the classical Kalman-Ho-Narendra
criterion which is well known in the linear case. },
DOI = {http://dx.doi.org/10.1016/0167-6911(86)90045-9}
}
@ARTICLE{MR863279,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Comments on: ``Some results on pole-placement and
reachability'' [Systems Control Lett. 6 (1986), no. 5, 325--328;
MR0821927 (87c:93032)] by P. K. Sharma},
YEAR = {1986},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {79--83},
VOLUME = {8},
ADDRESS = {Amsterdam, The Netherlands, The Netherlands},
KEYWORDS = {systems over rings, parametric classes of systems},
PUBLISHER = {Elsevier Science Publishers B. V.},
PDF = {../../FTPDIR/comments-sharma.pdf},
ABSTRACT = { We present various comments on a question about systems
over rings posed in a recent note by Sharma, proving that a ring R is
pole-assignable if and only if, for every reachable system (F,G), G
contains a rank-one summand of the state space. We also provide a
generalization to deal with dynamic feedback. },
DOI = {http://dx.doi.org/10.1016/0167-6911(86)90034-4}
}
@ARTICLE{HG,
AUTHOR = {E.D. Sontag},
JOURNAL = {IMA Journal of Mathematical Control and Information},
TITLE = {Continuous stabilizers and high-gain feedback},
YEAR = {1986},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {237--253},
VOLUME = {3},
KEYWORDS = {adaptive control, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/high-gain.pdf},
ABSTRACT = { A controller is shown to exist, universal for the
family of all systems of fixed dimension n, and m controls, which
stabilizes those systems that are stabilizable, if certain gains are
large enough. The controller parameters are continuous, in fact
polynomial, functions of the entries of the plant. As a consequence,
a result is proved on polynomial stabilization of families of
systems. }
}
@INPROCEEDINGS{PU86,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Info. Sci. and Systems, Princeton, 1986},
TITLE = {Controllability and linearized regulation},
YEAR = {1986},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {67--671},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{ROB2,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Int.Conf.on Robotics and Automation, San Francisco, April 1986},
TITLE = {Time-optimal control of manipulators},
YEAR = {1986},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1692--1697},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {robotics, optimal control},
PDF = {../../FTPDIR/1986_sontag_sussmann_time_optimal_manipulators_proc_robotics_and_automation_san_francisco.pdf},
ABSTRACT = { This paper studies time-optimal control questions for a
certain class of nonlinear systems. This class includes a large
number of mechanical systems, in particular, rigid robotic
manipulators with torque constraints. As nonlinear systems, these
systems have many properties that are false for generic systems of
the same dimensions. }
}
@INCOLLECTION{MR828315,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Linear algebra and its role in systems theory (Brunswick, Maine, 1984)},
PUBLISHER = {Amer. Math. Soc.},
TITLE = {An introduction to the stabilization problem for
parametrized families of linear systems},
YEAR = {1985},
ADDRESS = {Providence, RI},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {369--400},
SERIES = {Contemp. Math.},
OPTTYPE = {},
VOLUME = {47},
KEYWORDS = {systems over rings, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/ams85.pdf},
ABSTRACT = {This paper provides an introduction to definitions and
known facts relating to the stabilization of parametrized families of
linear systems using static and dynamic controllers. New results are
given in the rational and polynomial cases.}
}
@ARTICLE{MR808240,
AUTHOR = {B.W. Dickinson and E.D. Sontag},
JOURNAL = {IEEE Trans. Inform. Theory},
TITLE = {Dynamic realizations of sufficient sequences},
YEAR = {1985},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {670--676},
VOLUME = {31},
KEYWORDS = {realization theory, statistics, innovations,
sufficient statistics},
PDF = {../../FTPDIR/bd-suft-seq.pdf},
ABSTRACT = { Let Ul, U2, ... be a sequence of observed random
variables and (T1(U1),T2(Ul,U2),...) be a corresponding sequence of
sufficient statistics (a sufficient sequence). Under certain
regularity conditions, the sufficient sequence defines the
input/output map of a time-varying, discrete-time nonlinear system.
This system provides a recursive way of updating the sufficient
statistic as new observations are made. Conditions are provided
assuring that such a system evolves in a state space of minimal
dimension. Several examples are provided to illustrate how this
notion of dimensional minimality is related to other properties of
sufficient sequences. The results can be used to verify the form of
the minimum dimension (discrete-time) nonlinear filter associated
with the autoregressive parameter estimation problem. }
}
@ARTICLE{MR801975,
AUTHOR = {E.D. Sontag},
JOURNAL = {Inform. Process. Lett.},
TITLE = {Real addition and the polynomial hierarchy},
YEAR = {1985},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {115--120},
VOLUME = {20},
PDF = {../../FTPDIR/ra.pdf},
ABSTRACT = { The k-th alternation level of the theory of real
numbers under addition and order is log-complete for the k-th level
of the polynomial hierarchy. }
}
@INPROCEEDINGS{JHU85,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc.Conf. Info. Sci. and Systems, Johns Hopkins University, March 1985},
TITLE = {Further results on accessibility under sampling},
YEAR = {1985},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{IM1,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, 1985},
TITLE = {Image restoration and segmentation using the annealing
algorithm},
YEAR = {1985},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {768--773},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {image processing, optimization},
PDF = {../../FTPDIR/annealing.pdf},
ABSTRACT = { We consider the problem of estimating a signal, which
is known -- or assumed -- to be constant on each of the members of a
partition of a square lattice into m unknown regions, from the
observation of the signal plus Gaussian noise. This is a nonlinear
estimation problem, for which it is not appropriate to use the
conditional expectation as the estimate. We show that, at least in
principle, the "maximum iikelihood estimator" (MLE) proposed by Geman
and Geman lends itself to numerical computation using the annealing
algorithm. We argue that the MLE by itself can be, under certain
conditions (low signal to noise ratio), a very unsatisfactory
estimator, in that it does worse than just deciding that the signal
was zero. However, if combined with a rule which we propose, for
deciding when to use and when to ignore it, the MLE can provide a
reasonable suboptimal estimator. We then discuss preliminary
numerical data obtained using the annealing method. These results
indicate that: (a) the annealing algorithm performs remarkably well,
and (b) a criterion can be formulated in terms of quantities computed
from the observed image (without using a priori knowledge of the
signal-to-noise ratio) for deciding when to keep the MLE. }
}
@INPROCEEDINGS{ROB1,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, 1985},
TITLE = {Remarks on the time-optimal control of two-link
manipulators},
YEAR = {1985},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1646--1652},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {optimal control, robotics},
PDF = {../../FTPDIR/1985_sontag_sussmann_time_optimal_two_link_manipulators_CDC_fort_lauderdale.pdf}
}
@INCOLLECTION{MR792151,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Mathematical theory of networks and systems (Beer Sheva, 1983)},
PUBLISHER = {Springer},
TITLE = {An approximation theorem in nonlinear sampling},
YEAR = {1984},
ADDRESS = {London},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {806--812},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {58},
PDF = {../../FTPDIR/83mtns.pdf},
ABSTRACT = { We continue here our investigation into the
preservation of structural properties under the sampling of nonlinear
systems. The main new result is that, under minimal hypothesis, a
controllable system always satisfies a strong type of approximate
sampled controllability. }
}
@ARTICLE{MR735384,
AUTHOR = {C.A. Schwartz and B.W. Dickinson and E.D. Sontag},
JOURNAL = {Stochastics},
TITLE = {Characterizing innovations realizations for random
processes},
YEAR = {1984},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3-4},
PAGES = {159--172},
VOLUME = {11},
KEYWORDS = {statistics, innovations, sufficient statistics},
PDF = {../../FTPDIR/innovations.pdf},
ABSTRACT = { In this paper we are concerned with the theory of
second order (linear) innovations for discrete random processes. We
show that of existence of a finite dimensional linear filter
realizing the mapping from a discrete random process to its
innovations is equivalent to a certain semiiseparable structure of
the covariance sequence of the process. We also show that existence
of a finite dimensional realization (linear or nonlinear) of the
mapping from a process to its innovations implies that the process
have this serniseparable covariance sequence property. In particular,
for a stationary random process, the spectral density function must
be rational. }
}
@ARTICLE{MR768713,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {A concept of local observability},
YEAR = {1984},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {41--47},
VOLUME = {5},
KEYWORDS = {observability},
PDF = {../../FTPDIR/localobs.pdf},
ABSTRACT = { A notion of local observability, which is natural in
the context of nonlinear input/output regulation. is introduced. A
simple characterization is provided, a comparison is made with other
local nonlinear observability definitions. and its behavior under
constant-rate sampling is analyzed. }
}
@ARTICLE{MR730505,
AUTHOR = {E.D. Sontag},
JOURNAL = {Internat. J. Control},
TITLE = {An algebraic approach to bounded controllability of
linear systems},
YEAR = {1984},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {181--188},
VOLUME = {39},
KEYWORDS = {saturation, bounded inputs},
PDF = {../../FTPDIR/sic.pdf},
ABSTRACT = { In this note we present an algebraic approach to the
proof that a linear system with matrices (A,B) is null-controllable
using bounded inputs iff it is null-controllable (with unbounded
inputs) and all eigenvalues of A have nonpositive real parts
(continuous time) or magnitude not greater than one (discrete time).
We also give the analogous results for the asymptotic case. Finally,
we give an interpretation of these results in the context of local
nonlinear controllability. }
}
@ARTICLE{MR748279,
AUTHOR = {E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Parametric stabilization is easy},
YEAR = {1984},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {181--188},
VOLUME = {4},
KEYWORDS = {systems over rings, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/psis.pdf},
ABSTRACT = { A polynomially parametrized family of continuous-time
controllable linear systems is always stabilizable by polynomially
parametrized feedback. }
}
@INPROCEEDINGS{IMMER,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Las Vegas, Dec. 1984},
TITLE = {Remarks on input/output linearization},
YEAR = {1984},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {409--412},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
PDF = {../../FTPDIR/84cdc-immer.pdf},
ABSTRACT = { In the context of realization theory, conditions are
given for the possibility of simulating a given discrete time system,
using immersion and/or feedback, by linear or state-affine systems. }
}
@INCOLLECTION{MR783866,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Mathematical tools and models for control, systems analysis and signal processing, Vol. 3 (Toulouse/Paris, 1981/1982)},
PUBLISHER = {CNRS},
TITLE = {Remarks on the preservation of various controllability
properties under sampling},
YEAR = {1983},
ADDRESS = {Paris},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {623--637},
SERIES = {Travaux Rech. Coop. Programme 567},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {controllability, sampling, nonlinear systems,
real-analytic functions},
PDF = {../../FTPDIR/83belle-ille-sampling.pdf},
ABSTRACT = { This note studies the preservation of controllability
(and other properties) under sampling of a nonlinear system. More
detailed results are obtained in the cases of analytic systems and of
systems with finite dimensional Lie algebras. }
}
@ARTICLE{MR722954,
AUTHOR = {R.T. Bumby and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Stabilization of polynomially parametrized families of
linear systems. The single-input case},
YEAR = {1983},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {251--254},
VOLUME = {3},
KEYWORDS = {systems over rings, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/bum_reprint.pdf},
ABSTRACT = { Given a continuous-time family of finite dimensional
single input linear systems, parametrized polynomially, such that
each of the systems in the family is controllable, there exists a
polynomially parametrized control law making each of the systems in
the family stable. }
}
@ARTICLE{MR696908,
AUTHOR = {E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {A Lyapunov-like characterization of asymptotic
controllability},
YEAR = {1983},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {462--471},
VOLUME = {21},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/lyapunov_asymptotic_controllability_clf_sontag_siam1983.pdf},
ABSTRACT = { It is shown that a control system in Rn is
asymptotically controllable to the origin if and only if there exists
a positive definite continuous functional of the states whose
derivative can be made negative by appropriate choices of controls. }
}
@INPROCEEDINGS{JHU83,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Johns Hopkins Conf. on Info. Sci. and Systems, 1983},
TITLE = {Further remarks preservation of accessibility under
sampling},
YEAR = {1983},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {326--332},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{GNV2,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Dynamical Systems II},
PUBLISHER = {Academic Press, NY},
TITLE = {A characterization of asymptotic controllability},
YEAR = {1982},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {A. Bednarek and L. Cesari},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {645--648},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {control-Lyapunov functions},
PDF = {../../FTPDIR/1981.conference.paper.clf.sontag.book.1982.pdf},
ABSTRACT = {This paper was a conference version of the SIAM paper
that introduced the idea of control-Lyapunov functions for arbitrary
nonlinear systems. (The journal paper was submitted in 1981 but only
published in 1983.)}
}
@INCOLLECTION{MR837462,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Feedback control of linear and nonlinear systems (Bielefeld/Rome, 1981)},
PUBLISHER = {Springer},
TITLE = {Abstract regulation of nonlinear systems: stabilization},
YEAR = {1982},
ADDRESS = {Berlin},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {227--243},
SERIES = {Lecture Notes in Control and Inform. Sci.},
OPTTYPE = {},
VOLUME = {39}
}
@INCOLLECTION{MR735820,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {8th IFAC Triennial World Congress, Vol. 1 Kyoto, 1981},
PUBLISHER = {IFAC},
TITLE = {Linear systems over commutative rings: a (partial)
updated survey},
YEAR = {1982},
ADDRESS = {Laxenburg},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {325--330},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/1981_ifac_systems_over_rings_contrast_enhanced.pdf}
}
@ARTICLE{MR680321,
AUTHOR = {P.P. Khargonekar and E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {On the relation between stable matrix fraction
factorizations and regulable realizations of linear systems over
rings},
YEAR = {1982},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {627--638},
VOLUME = {27},
KEYWORDS = {systems over rings, systems over rings,
parametric classes of systems},
PDF = {../../FTPDIR/pk.pdf},
ABSTRACT = { Various types of transfer matrix factorizations are of
interest when designing regulators for generalized types of linear
systems (delay differential. 2-D, and families of systems). This
paper studies the existence of stable and of stable proper
factorizations, in the context of the thery of systems over rings.
Factorability is related to stabilizability and detectability
properties of realizations of the transfer matrix. The original
formulas for coprime factorizations (which are valid, in particular,
over the field of reals) were given in this paper. }
}
@ARTICLE{MR644949,
AUTHOR = {E.D. Sontag},
JOURNAL = {Pacific J. Math.},
TITLE = {Remarks on piecewise-linear algebra},
YEAR = {1982},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {183--201},
VOLUME = {98},
KEYWORDS = {hybrid systems, piecewise linear systems},
PDF = {../../FTPDIR/sontag_remarks_picewise_linear_algebra_pacific_j_math_1982.pdf},
ABSTRACT = { Algebraic study of functions defined by piecewise
linear (generally discontinuous) equations. File obtained by scanning
a reprint. }
}
@INPROCEEDINGS{82ciss,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1982},
TITLE = {Abstract regulation of nonlinear systems: Stabilization,
Part II},
YEAR = {1982},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {431-435},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {feedback stabilization}
}
@INPROCEEDINGS{SIC-CDC82,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982},
TITLE = {Small-input controllability},
YEAR = {1982},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INPROCEEDINGS{ACC,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Dec. and Control, Orlando, Dec. 1982},
TITLE = {Accessibility under sampling},
YEAR = {1982},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {discrete-time},
PDF = {../../FTPDIR/82cdc.pdf},
ABSTRACT = { This note addresses the following problem: Find
conditions under which a continuous-time (nonlinear) system gives
rise, under constant rate sampling, to a discrete-time system which
satisfies the accessibility property. }
}
@ARTICLE{MR601679,
AUTHOR = {R.T. Bumby and E.D. Sontag and H.J. Sussmann and
W. Vasconcelos},
JOURNAL = {J. Pure Appl. Algebra},
TITLE = {Remarks on the pole-shifting problem over rings},
YEAR = {1981},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {113--127},
VOLUME = {20},
KEYWORDS = {systems over rings, parametric classes of systems,
systems over rings},
PDF = {../../FTPDIR/bssv_reprint.pdf},
ABSTRACT = { Problems that appear in trying to extend linear control
results to systems over rings R have attracted considerable attention
lately. This interest has been due mainly to applications-oriented
motivations (in particular, dealing with delay-differential
equations), and partly to a purely algebraic interest. Given a square
n-matrix F and an n-row matrix G. pole-shifting problems consist in
obtaining more or less arbitrary characteristic polynomials for F+GK,
for suitable ("feedback") matrices K. A review of known facts is
given, various partial results are proved, and the case n=2 is
studied in some detail. }
}
@ARTICLE{MR686833,
AUTHOR = {E.D. Sontag},
JOURNAL = {Information and Control},
TITLE = {Conditions for abstract nonlinear regulation},
YEAR = {1981},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {105--127},
VOLUME = {51},
KEYWORDS = {feedback stabilization, nonlinear systems,
real-analytic functions},
PDF = {../../FTPDIR/1981_abstract_nonlinear_regulation_sontag.pdf},
ABSTRACT = { A paper that introduces a separation principle for
general finite dimensional analytic continuous-time systems, proving
the equivalence between existence of an output regulator (which is an
abstract dynamical system) and certain "0-detectability" and
asymptotic controllability assumptions. }
}
@ARTICLE{PLS,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {Nonlinear regulation: the piecewise linear approach},
YEAR = {1981},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {346--358},
VOLUME = {26},
KEYWORDS = {hybrid systems},
PDF = {../../FTPDIR/pls.pdf},
ABSTRACT = { Development of an approach to nonlinear control based
on mixtures of linear systems and finite automata. File obtained by
scanning. }
}
@INPROCEEDINGS{PK-CDC81,
AUTHOR = {P.P. Khargonekar and E.D. Sontag},
BOOKTITLE = {Proc. IEEE Conf.Dec. and Control, San Diego, Dec. 1981},
TITLE = {On the relation between stable matrix fraction
decompositions and regulable realizations of systems over rings},
YEAR = {1981},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {1006--1011},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {systems over rings, parametric classes of systems}
}
@TECHREPORT{BTL1,
AUTHOR = {E.D. Sontag and D.E. Stevenson},
INSTITUTION = {Bell Telephone Labs.},
TITLE = {Remarks on multi-server, multi-priority queuing models
related to MVS job scheduling},
YEAR = {1981},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {TM-81-45281-1},
OPTTYPE = {}
}
@INCOLLECTION{MR605868,
AUTHOR = {M. L. J. Hautus and E.D. Sontag},
BOOKTITLE = {Algebraic and geometric methods in linear systems theory (AMS-NASA-NATO Summer Sem., Harvard Univ., Cambridge, Mass., 1979)},
PUBLISHER = {Amer. Math. Soc.},
TITLE = {An approach to detectability and observers},
YEAR = {1980},
ADDRESS = {Providence, R.I.},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {99--135},
SERIES = {Lectures in Appl. Math.},
OPTTYPE = {},
VOLUME = {18},
KEYWORDS = {observability},
PDF = {../../FTPDIR/mh-observers.pdf},
ABSTRACT = { This paper proposes an approach to the problem of
establishing the existence of observers for deterministic dynamical
systems. This approach differs from the standard one based on
Luenberger observers in that the observation error is not required to
be Markovian given the past input and output data. A general abstract
result is given, which special- izes to new results for parametrized
families of linear systems, delay systems and other classes of
systems. Related problems of feedback control and regulation are also
studied. }
}
@INCOLLECTION{MR581716,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Systems analysis (Conf., Bordeaux, 1978)},
PUBLISHER = {Soc. Math. France},
TITLE = {On quasireachable realizations of a polynomial response},
YEAR = {1980},
ADDRESS = {Paris},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {207--217},
SERIES = {Astrisque},
OPTTYPE = {},
VOLUME = {75}
}
@ARTICLE{MR571759,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {On generalized inverses of polynomial and other matrices},
YEAR = {1980},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {514--517},
VOLUME = {25},
PDF = {../../FTPDIR/wgi.pdf},
ABSTRACT = { Necessary and sufficient conditions are given for a
matrix over a ring to admit a Moore-Penrose generalized inverse in a
weak sense. (Attached is also a Math Review with additional comments
on strong inverses.) }
}
@ARTICLE{MR561358,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Automat. Control},
TITLE = {On the length of inputs necessary in order to identify a
deterministic linear system},
YEAR = {1980},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {120--121},
VOLUME = {25},
PDF = {../../FTPDIR/80tac-number-inputs.pdf},
ABSTRACT = { The family of m-input, n-dimensional linear systems can
be globally Identified with a generic input sequence of length 2mn.
This bound is the best possible. A best bound is proved also for a
corresponding local identification problem. }
}
@INPROCEEDINGS{PLS-PU81,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc.Princeton Conf.on Information Sciences and Systems, Princeton, March 1980},
TITLE = {Nonlinear regulation, the piecewise linear approach},
YEAR = {1980},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
OPTPAGES = {},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {piecewise linear systems}
}
@INPROCEEDINGS{CF,
AUTHOR = {E.D. Sontag and H.J. Sussmann},
BOOKTITLE = {Proc. IEEE Conf. Decision and Control, Albuquerque, Dec.1980},
TITLE = {Remarks on continuous feedback},
YEAR = {1980},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {916--921},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {feedback stabilization},
PDF = {../../FTPDIR/80cdc.pdf},
ABSTRACT = { We show that, in general, it is impossible to stabilize
a controllable system by means of a continuous feedback, even if
memory is allowed. No optimality considerations are involved. All
state spaces are Euclidean spaces, so no obstructions arising from
the state space topology are involved either. For one dimensional
state and input, we prove that continuous stabilization with memory
is always possible. (This is an old conference paper, never published
in journal form but widely cited nonetheless. Warning: file is very
large, since it was scanned.) }
}
@BOOK{Springer79,
PUBLISHER = {Springer-Verlag},
TITLE = {Polynomial Response Maps},
YEAR = {1979},
AUTHOR = {E.D. Sontag},
ALTEDITOR = {},
ADDRESS = {Berlin},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
SERIES = {Lecture Notes in Control and Information Sciences},
VOLUME = {13},
KEYWORDS = {realization theory, discrete-time,
real algebraic geometry},
PAGES = {viii+168},
PDF = {../../FTPDIR/polynomial_response_maps.pdf},
ABSTRACT = { (This is a monograph based upon Eduardo Sontag's Ph.D.
thesis. The contents are basically the same as the thesis, except for
a very few revisions and extensions.) This work deals the realization
theory of discrete-time systems (with inputs and outputs, in the
sense of control theory) defined by polynomial update equations. It
is based upon the premise that the natural tools for the study of the
structural-algebraic properties (in particular, realization theory)
of polynomial input/output maps are provided by algebraic geometry
and commutative algebra, perhaps as much as linear algebra provides
the natural tools for studying linear systems. Basic ideas from
algebraic geometry are used throughout in system-theoretic
applications (Hilbert's basis theorem to finite-time observability,
dimension theory to minimal realizations, Zariski's Main Theorem to
uniqueness of canonical realizations, etc). In order to keep the
level elementary (in particular, not utilizing sheaf-theoretic
concepts), certain ideas like nonaffine varieties are used only
implicitly (eg., quasi-affine as open sets in affine varieties) or in
technical parts of a few proofs, and the terminology is similarly
simplified (e.g., "polynomial map" instead of "scheme morphism
restricted to k-points", or "k-space" instead of "k-points of an
affine k-scheme"). }
}
@ARTICLE{MR525830,
AUTHOR = {Y. Rouchaleau and E.D. Sontag},
JOURNAL = {J. Comput. System Sci.},
TITLE = {On the existence of minimal realizations of linear
dynamical systems over Noetherian integral domains},
YEAR = {1979},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {65--75},
VOLUME = {18},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/rouchaleau_sontag_minimal_realizations_noetherian_domains_jcss_1979.pdf},
ABSTRACT = { This paper studies the problem of obtaining minimal
realizations of linear input/output maps defined over rings. In
particular, it is shown that, contrary to the case of systems over
fields, it is in general impossible to obtain realizations whose
dimiension equals the rank of the Hankel matrix. A characterization
is given of those (Noetherian) rings over which realizations of such
dimensions can he always obtained, and the result is applied to
delay-differential systems. }
}
@ARTICLE{MR554018,
AUTHOR = {E.D. Sontag},
JOURNAL = {Kybernetika (Prague)},
TITLE = {On finitary linear systems},
YEAR = {1979},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {349--358},
VOLUME = {15},
KEYWORDS = {systems over rings, parametric classes of systems},
URL = {https://www.kybernetika.cz/content/1979/5/349/paper.pdf},
PDF = {../../FTPDIR/1979_kybernetica_finitary_linear_systems_sontag_reprint.pdf},
ABSTRACT = { An abstract operator approach is introduced, permitting
a unified study of discrete- and continuous-time linear control
systems. As an application, an algorithm is given for deciding if a
linear system can be built from any fixed set of linear components.
Finally, a criterion is given for reachability of the abstract
systems introduced, giving thus a unified proof of known reachability
results for discrete-time, continuous-time, and delay-differential
systems. }
}
@ARTICLE{MR516861,
AUTHOR = {E.D. Sontag},
JOURNAL = {SIAM J. Control Optim.},
TITLE = {On the observability of polynomial systems. I.
Finite-time problems},
YEAR = {1979},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {139--151},
VOLUME = {17},
KEYWORDS = {observability, observability, polynomial systems},
PDF = {../../FTPDIR/obs_observability_polynomial_systems_finite_time_sontag_reprint-siam1979.pdf},
ABSTRACT = { Different notions of observability are compared for
systems defined by polynomial difference equations. The main result
states that, for systems having the standard property of
(multiple-experiment initial-state) observability, the response to a
generic input sequence is sufficient for final-state determination.
Some remarks are made on results for nonpolynomial and/or
continuous-time systems. An identifiability result is derived from
the above. }
}
@ARTICLE{MR529666,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Circuits and Systems},
TITLE = {Realization theory of discrete-time nonlinear systems.
I. The bounded case},
YEAR = {1979},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {342--356},
VOLUME = {26},
KEYWORDS = {discrete-time systems, nonlinear systems,
realization theory, bilinear systems, state-affine systems},
PDF = {../../FTPDIR/state-affine-realiz.pdf},
ABSTRACT = { A state-space realization theory is presented for a
wide class of discrete time input/output behaviors. Although In many
ways restricted, this class does include as particular cases those
treated in the literature (linear, multilinear, internally bilinear,
homogeneous), as well as certain nonanalytic nonlinearities. The
theory is conceptually simple, and matrix-theoretic algorithms are
straightforward. Finite-realizability of these behaviors by
state-affine systems is shown to be equivalent both to the existence
of high-order input/output equations and to realizability by more
general types of systems. }
}
@ARTICLE{MR509164,
AUTHOR = {W. Dicks and E.D. Sontag},
JOURNAL = {J. Pure Appl. Algebra},
TITLE = {Sylvester domains},
YEAR = {1978},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {243--275},
VOLUME = {13},
PDF = {../../FTPDIR/wdicks.pdf},
ABSTRACT = { The inner rank of an m x n matrix A over a ring is
defined as the least integer r such that A can be expressed as the
product of an m x r and an r x n matrix. For example, over a (skew)
field this concept coincides with the usual notion of rank. This
notion is studied in this paper, and is related to Sylvester's law of
nullity and work by P.M. Cohn. }
}
@ARTICLE{2D,
AUTHOR = {E.D. Sontag},
JOURNAL = {IEEE Trans. Acoustics, Speech, and Signal Processing},
TITLE = {On first-order equations for multidimensional filters},
YEAR = {1978},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {480--482},
VOLUME = {26},
PDF = {../../FTPDIR/2D.pdf},
ABSTRACT = { A construction is given to obtain first-order equation
representations of a multidimensional filter, whose dimension is of
the order of the degree of the transfer function. }
}
@ARTICLE{MR0490149,
AUTHOR = {E.D. Sontag},
JOURNAL = {Information and Control},
TITLE = {On split realizations of response maps over rings},
YEAR = {1978},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {23--33},
VOLUME = {37},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/sontag_minimal_split_realizations_systems_over_rings_information_control1978.pdf},
ABSTRACT = { This paper deals with observability properties of
realizations of linear response maps defined over commutative rings.
A characterization is given for those maps which admit realizations
which are simultaneously reachable and observable in a strong sense.
Applications are given to delay-differential systems. }
}
@INPROCEEDINGS{JHU78,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Proc. Conf. Inform. Sci. and Systems, John Hopkins Univ. (1978)},
TITLE = {Algebraic-geometric methods in the realization of
discrete-time systems},
YEAR = {1978},
OPTADDRESS = {},
OPTCROSSREF = {},
OPTEDITOR = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTORGANIZATION = {},
PAGES = {158--162},
OPTPUBLISHER = {},
OPTSERIES = {},
OPTVOLUME = {}
}
@INCOLLECTION{GNV1,
AUTHOR = {E.D. Sontag},
BOOKTITLE = {Dynamical Systems},
PUBLISHER = {Academic Press, New York},
TITLE = {On the internal realization of nonlinear behaviors},
YEAR = {1977},
OPTADDRESS = {},
OPTCHAPTER = {},
OPTCROSSREF = {},
OPTEDITION = {},
EDITOR = {A. Bednarek and L. Cesari},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {93--497},
OPTSERIES = {},
OPTTYPE = {},
OPTVOLUME = {}
}
@ARTICLE{MR0472151,
AUTHOR = {E.D. Sontag},
JOURNAL = {Math. Systems Theory},
TITLE = {The lattice of minimal realizations of response maps
over rings},
YEAR = {1977},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {169--175},
VOLUME = {11},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/lat.pdf},
ABSTRACT = { A lattice characterization is given for the class of
minimal-rank realizations of a linear response map defined over a
(commutative) Noetherian integral domain. As a corollary, it is
proved that there are only finitely many nonisomorphic minimal-rank
realizations of a response map over the integers, while for delay
-differential systems these are classified by a lattice of subspaces
of a finite-dimensional real vector space. }
}
@ARTICLE{MR0427298,
AUTHOR = {E.D. Sontag and Y. Rouchaleau},
JOURNAL = {C. R. Acad. Sci. Paris Sr. A-B},
TITLE = {Sur les anneaux de Fatou forts},
YEAR = {1977},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {5},
PAGES = {A331--A333},
VOLUME = {284},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/fatou.pdf},
ABSTRACT = { It is well known that principal rings are strong Fatou
rings. We construct here a more general type of strong Fatou rings.
We also prove that the monoid of divisor classes of a noetherian
strong Fatou ring contains only the zero element, and that the
dimension of such a ring is at most two. }
}
@PHDTHESIS{thesis,
AUTHOR = {E.D. Sontag},
SCHOOL = {Univ. of Florida, Advisor: R.E. Kalman},
TITLE = {On the internal realization of polynomial response maps},
YEAR = {1976},
OPTADDRESS = {},
OPTMONTH = {},
OPTNOTE = {},
OPTTYPE = {}
}
@ARTICLE{SSR,
AUTHOR = {E.D. Sontag},
JOURNAL = {Ricerche di Automatica},
TITLE = {Linear systems over commutative rings: A survey},
YEAR = {1976},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1--34},
VOLUME = {7},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/ssr.pdf},
ABSTRACT = { An elementary presentation is given of some of the main
motivations and known results on linear systems over rings, including
questions of realization and control. The analogies and differences
with the more standard case of systems over fields are emphasized
throughout. }
}
@ARTICLE{MR0417241,
AUTHOR = {E.D. Sontag},
JOURNAL = {J. Pure Appl. Algebra},
TITLE = {On finitely accessible and finitely observable rings},
YEAR = {1976},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {97--104},
VOLUME = {8},
KEYWORDS = {systems over rings, parametric classes of systems,
observability, noncommutative rings},
PDF = {../../FTPDIR/ncr.pdf},
ABSTRACT = { Two classes of rings which occur in linear system
theory are introduced and compared. Characterizations of one of them
are given in terms, of integral extensions (every finite extension of
R is integral) and Cayley--Hamilton type matrix condition. A
comparison is made in the case of no zero-divisors with Ore domains. }
}
@ARTICLE{MR0479498,
AUTHOR = {E.D. Sontag and Y. Rouchaleau},
JOURNAL = {Nonlinear Anal.},
TITLE = {On discrete-time polynomial systems},
YEAR = {1976},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {1},
PAGES = {55--64},
VOLUME = {1},
KEYWORDS = {identifiability, observability, polynomial systems,
realization theory, discrete-time},
PDF = {../../FTPDIR/polynomialsystems76.pdf},
ABSTRACT = { Considered here are a type of discrete-time systems
which have algebraic constraints on their state set and for which the
state transitions are given by (arbitrary) polynomial functions of
the inputs and state variables. The paper studies reachability in
bounded time, the problem of deciding whether two systems have the
same external behavior by applying finitely many inputs, the fact
that finitely many inputs (which can be chosen quite arbitrarily) are
sufficient to separate those states of a system which are
distinguishable, and introduces the subject of realization theory for
this class of systems. }
}
@ARTICLE{MR0452844,
AUTHOR = {E.D. Sontag},
JOURNAL = {Math. Systems Theory},
TITLE = {On linear systems and noncommutative rings},
YEAR = {1975},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {4},
PAGES = {327--344},
VOLUME = {9},
KEYWORDS = {systems over rings, parametric classes of systems},
PDF = {../../FTPDIR/ls-ncr.pdf},
ABSTRACT = { This paper studies some problems appearing in the
extension of the theory of linear dynamical systems to the case in
which parameters are taken from noncommutative rings. Purely
algebraic statements of some of the problems are also obtained.
Through systems defined by operator rings, the theory of linear
systems over rings may be applied to other areas of automata and
control theory; several such applications are outlined. }
}
@ARTICLE{jcss75rat,
AUTHOR = {E.D. Sontag},
JOURNAL = {J. Comput. System Sci.},
TITLE = {On some questions of rationality and decidability},
YEAR = {1975},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {3},
PAGES = {375--381},
VOLUME = {11},
KEYWORDS = {theory of computing and complexity},
PDF = {../../FTPDIR/rat-dec.pdf},
ABSTRACT = { Some results are given in the theory of rational power
series over a broad class of semirings. In particular, it is shown
that for unambiguous sets the notion of rationality is independent of
the semiring over which representations are defined. The
undecidability of the rationality of probabilistic word functions is
also established. }
}
@BOOK{AI,
PUBLISHER = {PROLAM, Buenos Aires},
TITLE = {Temas de Inteligencia Artificial},
YEAR = {1972},
AUTHOR = {E.D. Sontag},
ALTEDITOR = {},
OPTADDRESS = {},
OPTEDITION = {},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
OPTSERIES = {},
OPTVOLUME = {},
KEYWORDS = {machine learning, artificial intelligence,
neural networks},
PDF = {../../FTPDIR/sontag_1972_temas_inteligencia_artificial_ocr_searchable_adobe_online.pdf},
ABSTRACT = {Textbook on Artificial Intelligence. (Libro de texto con
introduccion a la inteligencia artificial)}
}