Optimal Tracking with Preview for Linear Continuous-Time Markovian Jump Systems

Abstract

In order to design tracking control systems for a class of systems with rapid or abrupt changes, it is effective in improving tracking performance to construct preview control systems considering future information of reference signals. In this paper we study the optimal tracking problems with preview for a class of linear continuous-time Markovian jump systems. Our systems are described by the switching systems with Markovian mode transition. The necessary and sufficient conditions for the solvability of our LQ tracking problem are given by coupled Riccati differential equations with terminal conditions. Correspondingly feedforward compensators introducing future information are given by coupled differential equations with terminal conditions. We consider three different tracking problems depending on the property of the reference signals. Finally we give numerical examples.