Publications about 'adaptive control'
Articles in journal or book chapters
  1. M.A. Al-Radhawi, M. Sadeghi, and E.D. Sontag. Long-term regulation of prolonged epidemic outbreaks in large populations via adaptive control: a singular perturbation approach. IEEE Control Systems Letters, 6:578-583, 2022. [PDF] Keyword(s): epidemiology, COVID-19, COVID, systems biology.
    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.

  2. L. Moreau and E.D. Sontag. Balancing at the border of instability. Phys. Rev. E (3), 68(2):020901, 4, 2003. [PDF] Keyword(s): bifurcations, adaptive control.
    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.

  3. L. Moreau, E.D. Sontag, and M. Arcak. Feedback tuning of bifurcations. Systems Control Lett., 50(3):229-239, 2003. [PDF] Keyword(s): bifurcations, adaptive control.
    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.

  4. D. Liberzon, A. S. Morse, and E.D. Sontag. Output-input stability and minimum-phase nonlinear systems. IEEE Trans. Automat. Control, 47(3):422-436, 2002. [PDF] Keyword(s): input to state stability, detectability, minimum-phase systems, ISS, nonlinear control, minimum phase, adaptive control.
    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.

  5. E.D. Sontag. Continuous stabilizers and high-gain feedback. IMA Journal of Mathematical Control and Information, 3:237-253, 1986. [PDF] Keyword(s): adaptive control, systems over rings.
    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.

Conference articles
  1. D. Liberzon, A.S. Morse, and E.D. Sontag. A new definition of the minimum-phase property for nonlinear systems, with an application to adaptive control. In Proc. IEEE Conf. Decision and Control, Sydney, Dec. 2000, IEEE Publications, 2000, pages 2106-2111, 2000.



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