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

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.