Robust optimal periodic control using guaranteed Euler's method

Abstract

In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler approximate solutions for the system extended with bounded perturbations. The main result gives a simple condition on the perturbed system for guaranteeing the existence of a stable limit cycle of the unperturbed system. An illustrative numerical example is provided which demonstrates the applicability of the method.

This is the author version of the manuscript of the same name published in the proceedings of the 2021 American Control Conference (ACC 2021)