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
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 NeuroPSI - Institut des Neurosciences Paris-Saclay

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.

Domains: Neurons and Cognition [q-bio.NC]; Dynamical Systems [math.DS]

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⟩