Primal-Dual Reinforcement Learning for Zero-Sum Games in the Optimal Tracking Control

The two-player zero-sum game method for solving optimal tracking problems with external disturbance has been extensively explored. However, challenges such as the selection of initial admissible policies and learning errors diminish the accuracy of the Nash equilibrium, even limiting the method's application to some extent. The proposed model-free primal-dual reinforcement learning algorithm utilizes state-input trajectories generated by a set of linearly independent initial vectors to obtain Nash equilibrium without the need for probing noise. Admissible policies for both players are treated as a non-convex constraint and solved from a primal-dual perspective. Simulation results for an inverter confirm that the proposed unbiased learning method not only exhibits superior tracking performance but also demonstrates a faster convergence speed.