Reinforcement Q-learning algorithm for <i> H _∞ </i> tracking control of discrete-time Markov jump systems

In this paper, the $ H_{\infty } $ H∞ tracking control problem of linear discrete-time Markov jump systems is studied by using the data-based reinforcement learning method. Specifically, a new performance index function is established by using Markov chain and weighted sum technique, and thus the tracking game algebraic Riccati equation with weight vector and discount factor is obtained. A Q-learning algorithm is proposed to solve the tracking game algebra Riccati equation problem online without knowing the information of the system model. In addition, the convergence analysis of the algorithm is given, and it is proved that the added probing noise will not bias the algorithm. Finally, two simulation examples are given to verify the effectiveness of the proposed algorithm.