Online optimal solutions for multi-player nonzero-sum game with completely unknown dynamics

In this paper, a data-driven approximate neural network (NN) learning scheme is developed to solve the multi-player nonzero-sum (NZS) game problem with completely unknown system dynamics. An augmented NN identifier based on a new parameter estimation algorithm is first established to approximate the completely unknown system dynamics. Then approximated dynamic programming (ADP) with neural networks is constructed to approximate the optimal solutions of the coupled Hamilton-Jacobi equations for each player. The approximated NN value functions are then used to synchronously calculate the optimal control policies for every player. The identifier and ADP NN weights are online updated with the system input-output data based on a novel adaptive law, which could achieve a faster convergence speed. Moreover, the convergence of all NN weights and the stability of the closed-loop system are proved based on the Lyapunov approach. Finally, a dual-driven servo motor system and a three-player nonlinear game system are simulated to verify the feasibility of the developed methods.