A nonlinear multi-player non-zero-sum differential game with state constraints and input delay

This paper investigates a nonlinear multi-player non-zero-sum differential game with state constraints and input delay. To solve this problem, this paper constructs a neural network (NN) framework to approximate the solution of the Hamilton-Jacobi-Isaacs equation. The adaptive dynamic programming method is utilized where each player only needs one critic NN. To solve the issue of state saturation and input delay, this paper develops a novel state constraints mechanism for the differential game to make the states within the predetermined constraint set. Then, a future predictor is employed to compensate for the input delay. The condition that estimated states of agents having nonlinear dynamics with the predictor converge to the real state is derived. With these treatments, the system is more in line with real-world applications. Moreover, the stability of the system is also analyzed using the Lyapunov theorem. Simulation examples are given to validate the efficiency of the presented methods.