Optimization of Markov jump linear system with controlled modes jump probabilities

Abstract

The optimal control of a Markov jump linear quadratic model with controlled jump probabilities of modes is investigated. Two kinds of mode control policies, i.e., open-loop control policy and closed-loop control policy, are considered. Using the concepts of policy iteration and performance potential, the sufficient condition needed for the optimal closed-loop control policy to perform better than the optimal open-loop control policy is proposed. The condition is helpful for the design of an optimal controller. Furthermore, an efficient algorithm to construct a closed-loop control policy, which is better than the optimal open-loop control policy, is given with policy iteration.