H∞ Tracking learning control for discrete-time Markov jump systems: A parallel off-policy reinforcement learning

This paper deals with the H infinity tracking control problem for a class of linear discrete-time Markov jump systems, in which the knowledge of system dynamics is not required. First, combined with reinforcement learning, a novel Bellman equation and the augmented coupled game algebraic Riccati equation are presented to derived the optimal control policy for the augmented discrete-time Markov jump systems. Moreover, based on the augmented system, a newly constructed system is given to collect the input and output data, which solves the problem that the coupling term in the discrete-time Markov jump systems is difficult to solve. Subsequently, a novel model-free algorithm is designed that does not need the dynamic information of the original system. Finally, a numerical example is given to verify the effectiveness of the proposed approach.