Game-based Optimized Backstepping Control for Strict-feedback Systems With Input Constraints

In this paper, the optimal backstepping control method based on game theory is designed for strict feedback nonlinear systems with input saturation. In order to improve the robustness of the system, the zero-sum game problem of control input and disturbance for strict feedback systems is studied in this paper. Specifically, reinforcement learning (RL) is used to obtain the Nash equilibrium solution of the subsystem corresponding to the virtual control input and the virtual disturbance based on the HJB equation. By using the recursive process of backstepping, the controller of the tracking game problem between the control input and the disturbance of the high-order system is designed. In addition, according to the Lyapunov stability theory, it is proved that all internal signals of the closed-loop systems are uniformly ultimately bounded (UUB). Finally, simulation results are provided to illustrate the validity of the proposed method.