On the numerical solution of the control problem of switched linear systems

Abstract

This paper presents a method to compute an epsilon-optimal solution of the control problem of switched linear systems. A difficulty that emerges in the evalution of the optimal solution is that the cardinality of the solution set increases exponentially as long as the time-horizon increases linearly, which turns the problemintractable when the horizon is sufficiently large. We propose a numerical method to overcome such difficulty, in the sense that our approach allows the evalution of epsilon-optimal solutions with corresponding sets that do not increase exponentially.