1. M.A. Al-Radhawi, D. Del Vecchio, and E.D. Sontag. Identifying competition phenotypes in synthetic biochemical circuits. IEEE Control Systems Letters, 7:211-216, 2023. Note: (Online published in 2022; in print 2023.). [PDF] Keyword(s): Resource competition, model discrimination, synthetic biology, system identification. 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.




2. J. Hanson, M. Raginsky, and E.D. Sontag. Learning recurrent neural net models of nonlinear systems. Proc. of Machine Learning Research, 144:1-11, 2021. [PDF] Keyword(s): machine learning, empirical risk minimization, recurrent neural networks, dynamical systems, continuous time, system identification, statistical learning theory, generalization bounds. 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.




3. M. A. Dahleh, E.D. Sontag, D. N. C. Tse, and J. N. Tsitsiklis. Worst-case identification of nonlinear fading memory systems. Automatica, 31(3):503-508, 1995. [PDF] [doi:http://dx.doi.org/10.1016/0005-1098(94)00131-2] Keyword(s): information-based complexity, fading-memory systems, stability, system identification, structured uncertainty. 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.

1. F. Menolascina, R. Stocker, and E.D. Sontag. In-vivo identification and control of aerotaxis in Bacillus subtilis. In Proc. IEEE Conf. Decision and Control, Dec. 2016, pages 764-769, 2016. [PDF] Keyword(s): identification, systems biology, aerotaxis, B. subtilis. 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.




2. M.A. Dahleh, E.D. Sontag, D.N.C. Tse, and J.N. Tsitsiklis. Worst-case identification of nonlinear fading memory systems. In Proc. Amer. Automatic Control Conf., Chicago, June 1992, pages 241-245, 1992. [PDF] Keyword(s): information-based complexity, fading-memory systems, stability, system identification, structured uncertainty. Abstract:

   Preliminary version of paper published in Automatica in 1995.

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