Reinforcement Q-Learning and Non-Zero-Sum Games Optimal Tracking Control for Discrete-Time Linear Multi-Input Systems
Jingang Zhao · 2023
This paper studies the optimal tracking control problem of discrete-time linear multi-input systems from the perspective of Non-Zero-Sum Games (NZSG) using reinforcement Q-learning technique. Firstly, an augmented multi-input systems is constructed by combining the original multi-input systems and the reference trajectory dynamics. Then, the original optimal tracking control problem can be transformed into the NZSG optimal control problem of the constructed augmented multi-input systems. In order to obtain the Nash equilibrium solution of the NZSG optimal control problem, a Q-function is introduced and an reinforcement Q-learning algorithm is designed to learn the Nash equilibrium solution. The convergence of the reinforcement Q-learning algorithm is also given. Finally, a simulation example is given to verify the effectiveness of the proposed reinforcement Q-learning algorithm.