An Optimal Tracking Control Method with Q-learning for Discrete-time Linear Switched System

In this paper, a novel approach combining Q-learning method and two-stage optimization is proposed to solve linear quadratic tracking (LQT) problem for unknown discrete-time switched system. An augmented system consisting of switched subsystem and reference trajectory is built and Q-learning method is introduced to identify each subsystem without requiring any knowledge of augmented system state dynamics. Then, based on the optimal control laws for each subsystem obtained by Q-learning in advance, the optimal hybrid control law including switching mode and control input is obtained by the two-stage optimization framework. Furthermore, the optimality of the algorithm is proved. Finally, a simulation case is used to testify the effectiveness of the proposed algorithm.