Adaptive control of Lipschitz time-delay systems by sigma modification with application to neuronal population dynamics. (English) Zbl 1485.93294
Summary: Adaptive control using the \(\sigma \)-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.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93C43 | Delay control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
Keywords:
time-delay systems; adaptive control; sigma modification; stability in the mean; neuronal populationsReferences:
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