1. Adaptive control of Lipschitz time-delay systems by sigma modification with application to neuronal population dynamics
- Author
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Alain Destexhe, Jakub Orlowski, Antoine Chaillet, Mario Sigalotti, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Institut des Neurosciences Paris-Saclay (NeuroPSI), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), This paper has received support from the Institute for Control and Decision of Paris Saclay (iCODE), France and Digiteo, France. AD was supported by the CNRS, France and the European Commission (Human Brain Project H2020-945539)., Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
- Subjects
0209 industrial biotechnology ,Time-delay systems ,Adaptive control ,General Computer Science ,Computer science ,Mechanical Engineering ,Dynamics (mechanics) ,Sigma ,02 engineering and technology ,Dissipation ,Sigma modification ,Lipschitz continuity ,Nonlinear system ,Neuronal populations ,020901 industrial engineering & automation ,Quadratic equation ,Control and Systems Engineering ,Control theory ,Stability in the mean ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Electrical and Electronic Engineering ,Neuronal population - Abstract
International audience; Adaptive control using the -modification provides an easily implementable way to stabilize systems with uncertain or fluctuating parameters. Motivated by a specific application from neuroscience, we extend here this methodology to nonlinear time-delay systems ruled by globally Lipschitz dynamics. In order to make the result more handy in practice, we provide an explicit construction of a Lyapunov–Krasovskii functional (LKF) with linear bounds and strict dissipation rate based on the knowledge of an LKF with quadratic bounds and point-wise dissipation rate. When applied to a model of neuronal populations involved in Parkinson’s disease, the benefits with respect to a pure proportional stabilization scheme are discussed through numerical simulations.
- Published
- 2022