Optimal tracking control for non-zero-sum games of linear discrete-time systems via off-policy reinforcement learning

In this article, a model-free off-policy reinforcement learning algorithm is applied to address the optimal tracking problem based on multiplayer non-zero-sum games for discrete-time linear systems. In contrast to the traditional method and the policy iteration method for solving the optimal tracking problems, the proposed algorithm operates with the system data rather than the knowledge of the system dynamics. For performing the proposed algorithm, an auxiliary augmented system is constructed via assembling the original system and the reference trajectory while a discount factor is introduced into the performance indexes. It is analyzed that the solutions of the proposed algorithm converge to the Nash equilibrium and the result is not influenced by the probing noise. Two simulations are presented to verify the feasibility and effectiveness of the proposed algorithm.