AN APPROACH TO SWITCHED SYSTEMS OPTIMAL CONTROL BASED ON PARAMETERIZATION OF THE SWITCHING INSTANTS

Abstract

This paper provides a viable general approach to switched systems optimal control. Such optimal control problems require the solutions of not only optimal continuous inputs but also optimal switching sequences. Many practical problems only involve optimization where the number of switchings and the sequence of active subsystems are given. This is stage 1 of the two stage optimization methodology proposed by the authors in previous papers. In order to solve stage 1 problems, the derivatives of the optimal cost with respect to the switching instants need to be known. In (Xu and Antsaklis, 2001), we proposed an approach for solving a special class of such problems, namely, general switched linear quadratic problems. In this paper, the idea of (Xu and Antsaklis, 2001) is extended to general switched systems optimal control problems and an approach is proposed for solving them. The approach first transcribes a stage 1 problem into an equivalent problem parameterized by the switching instants and then the values of the derivatives are obtained based on the solution of a two point boundary value differential algebraic equation formed by the state, costate, stationarity equations, the boundary and continuity conditions and their differentiations. Examples are shown to illustrate the results in the paper.