Predefined time reinforcement learning algorithm for continuous nonlinear system under zero-sum game

In this paper, a reinforcement learning algorithm with predefined time convergence is proposed for continuous nonlinear systems under a zero-sum game. On the basis of system dynamics, the performance index is formulated, and the critic-only neural network is designed to approximate the value function according to the Bellman optimality principle. By solving the Hamilton-Jacobi-Isaacs equation, the approximate optimal control strategy and the corresponding worst-case disturbance are obtained indirectly. To ensure the convergence of the predefined time, a specially designed loss function is introduced in the reinforcement learning framework. The stability and weight convergence of the closed-loop nonlinear system are analyzed, and the system is guaranteed to converge within a predetermined time. Finally, the simulation results verify the effectiveness of the proposed method.