H∞ tracking control for perturbed discrete-time systems using On/Off policy Q-learning algorithms

Abstract

The widely studied $H_{\infty }$ zero-sum game problem guarantees the integration of external disturbance into the optimal control problem. In this article, two model-free Q-learning algorithms based on $H_{\infty }$ tracking control are proposed for perturbed discrete-time systems in the presence of external disturbance. Moreover, modification of the output optimal control problem is also made. For the optimal tracking control problem, the existence of a discount factor is necessary to guarantee the final value of the cost function, and the Ricatti equation is modified. With the aid of the deviation between Q functions at two consecutive times and the original principle of Off/On policy, the consideration of $H_{\infty }$ zero-sum game problem, two On/Off Q-learning algorithms based on $H_{\infty }$ tracking control are proposed. Then, by computing the Q function, the influence of probing noise on the Q function is considered. The analysis of solution equivalence proves that convergence and tracking are guaranteed in the proposed algorithm. Eventually, simulation studies are carried out on F-16 aircraft to assess the validity of the presented control schemes.