A sampling-based approach for handling delays in continuous and hybrid systems

Abstract

Delays in feedback dynamics of coupled dynamical systems arise regularly, especially in embedded control where the physical plant and the controller continuously interact through digital networks. Systems featuring delays are however notoriously difficult to analyze. Consequently, formal analysis often addresses simplified, delay-free substitute models, risking negligence of the adverse impact of delay on control performance. In this ongoing work, we demonstrate that for continuous systems such as delay differential equations, a major part of the delay-induced complexity can be reduced effectively when adding natural constraints to the model of the delayed feedback channel, namely that it transports a band-limited signal and implements a non-punctual, distributed delay. The reduction is based on a sampling approach which is applicable when the above conditions on the feedback are satisfied. We further discuss the possibilities of lifting this method to mixed discrete-continuous dynamics of delayed hybrid systems and the open issues thereof.