Nonlinear hybrid control of phase models for coupled oscillators

We present a new approach to the problem of desynchronization of a population of all-to-all coupled oscillators. Motivated by Deep Brain Stimulation treatment of Parkinson's Disease, the objective is to break this synchrony in the fullest measure by means of a control input only applied to one of the oscillators. Specifically, nonlinear hybrid control is proposed as a novel method for robust global asymptotic stabilization of the splay state. The problem setup is presented in a general way, and a simple example is solved that gives an idea of how this method might be applied in practice.