Adaptive control of Lipschitz time-delay systems by sigma modification with application to neuronal population dynamics - Archive ouverte HAL Access content directly
Journal Articles Systems and Control Letters Year : 2022

Adaptive control of Lipschitz time-delay systems by sigma modification with application to neuronal population dynamics

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Abstract

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.
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Dates and versions

hal-03468630 , version 1 (03-02-2022)

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Jakub Orlowski, Antoine Chaillet, Alain Destexhe, Mario Sigalotti. Adaptive control of Lipschitz time-delay systems by sigma modification with application to neuronal population dynamics. Systems and Control Letters, 2022, 159, pp.105082. ⟨10.1016/j.sysconle.2021.105082⟩. ⟨hal-03468630⟩
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