Robust optimal periodic control using guaranteed Euler's method

TL;DR

This paper develops a method for designing robust optimal periodic controls for switched systems, ensuring stability despite perturbations, using Euler's method and dynamic programming, with practical numerical validation.

Contribution

It introduces a simple stability condition for perturbed systems and applies Euler's method to guarantee the existence of stable limit cycles in optimal control.

Findings

Guarantees the existence of stable limit cycles under perturbations.

Provides a stability condition based on Euler's approximation.

Demonstrates applicability through a numerical example.

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.