Dynamic Programming based Optimal Control of Discrete Time Switched Linear Systems

Optimal control of switched systems deals with the design of an optimal switching signal and control input for switched systems. In this paper, an optimal switching feedback law with a finite number of switching is proposed for an asymptotically stabilizable discrete-time switched linear system with at least one controllable subsystem. The algorithm uses dynamic programming based approach for minimizing the quadratic cost.

I. Introduction

Switched systems are dynamical systems that consist of a finite number of subsystems or modes and some switching law that governs switching among them [1]. The switching signal which is piece-wise constant and infinite dimensional, is the logical rule that decides the switching between the subsystems. In optimal control of switched systems, one has to design the optimal switching signal which decides the active subsystem and the optimal control input for the active subsystem in such a way that the cost function J is minimized. The interaction between the switching signal and the control input makes the problem complex and impossible to solve analytically even for simple systems.