Noncooperative Game Based on Iteration Learning for Nonlinear Optimal Regulation

The disturbance is an uncertain factor affecting the stable operation of the system. In addressing the optimal control issue of nonlinear systems with disturbances, reinforcement learning, zero-sum game, and optimal control are integrated to establish a two-player zero-sum game algorithm based on iterative learning in this article. First, the optimal control issue of nonlinear systems with disturbances is modeled as a two-player zero-sum game problem based on the Markov decision process. Then, an offline learning mechanism using a single critic network is designed to seek the Nash equilibrium strategy. The convergence of the proposed algorithm is also rigorously analyzed. Finally, the simulation experiment verifies the effectiveness of the proposed algorithm in solving the optimal control issue of disturbed systems.