Zero-sum game optimal control for the nonlinear switched systems based on heuristic dynamic programming

In this article, the zero-sum game problem of control and disturbance is studied for discrete affine nonlinear switched systems with unknown dynamical models. A two-level heuristic dynamic programming iterative algorithm for solving the zero-sum game problem is proposed, which can be used to solve the Hamilton-Jacobi-Isaacs equation associated with the optimal regulation control problem. The convergence analysis based on the value function and control strategy is given. For algorithm implementation, neural networks are used to approximate the control strategy, disturbance strategy, and value function of the game dynamic programming, respectively. A model network is used to approximate the system states with an unknown dynamical model. The iterative algorithm steps are given. Finally, the validity of the method is verified by simulation examples.