Reinforcement Q-learning and Optimal Tracking Control of Unknown Discrete-time Multi-player Systems Based on Game Theory

This paper studies the fully cooperative game tracking control problem (FCGTCP) for a class of discrete-time multi-player linear systems with unknown dynamics. The reference trajectory is generated by a command generator system. An augmented multi-player systems composed of the origin multi-player systems and the command generator system is constructed, and an exponential discounted cost function is introduced to derive an augmented fully cooperative game tracking algebraic Riccati equation (FCGTARE). When the system dynamics are known, a model-based policy iteration (PI) algorithm is proposed to solve the augmented FCGTARE. Furthermore, to relax the system dynamics, an online reinforcement Q-learning algorithm is designed to obtain the solution to the augmented FCGTARE. The convergence of designed online reinforcement Q-learning algorithm is proved. Finally, two simulation examples are given to verify the validity of the model-based PI algorithm and online reinforcement Q-learning algorithm.