Adaptive scheme for pathological oscillations disruption in a delayed neuronal population model

Jakub Orłowski 1, 2 Antoine Chaillet 1 Mario Sigalotti 2, 3 Alain Destexhe 4
1 L2S - Laboratoire des signaux et systèmes
2 CaGE - Control And GEometry
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 Neuro-PSI - Institut des Neurosciences de Paris-Saclay
Abstract : Motivated by improved ways to disrupt brain oscillations linked to Parkinson's disease, we propose an adaptive output feedback strategy for the stabilization of nonlinear time-delay systems evolving on a bounded set. To that aim, using the formalism of input-to-output stability (IOS), we first show that, for such systems, internal stability guarantees robustness to exogenous disturbances. We then use this feature to establish a general result on scalar adaptive output feedback of time-delay systems inspired by the "σ-modification" strategy. We finally apply this result to a delayed neuronal population model and assess numerically the performance of the adaptive stimulation.
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Submitted on : Saturday, December 15, 2018 - 7:30:01 PM
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Jakub Orłowski, Antoine Chaillet, Mario Sigalotti, Alain Destexhe. Adaptive scheme for pathological oscillations disruption in a delayed neuronal population model. 57th IEEE Conference on Decision and Control (CDC 2018), Dec 2018, Miami Beach, United States. ⟨hal-01956472⟩

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