Optimized adaptive tracking control for nonlinear differential game systems

This paper designed a tracking control method for nonlinear differential game systems by using the adaptive dynamic programming (ADP) technique. In contrast to existing results of tracking control, the optimization problem with finite-horizon constrains is considered. To realize both trajectory tracking and performance optimizing, we isolated an error function from the optimal cost function. In general, the optimal controller for the nonlinear differential game system is unavailable since the nonlinear Hamilton-Jacobi-Issacs (HJI) equation is even impossible to be solved by analytical methods. Therefore, neural networks (NNs) are applied to estimate unknown optimal cost function and control strategies. Then, sufficient conditions are derive to demonstrate the closed-loop tracking error system and weight approximation errors are uniformly ultimately bounded (UUB). Finally, the validity of the results obtained are proved by introducing a numerical example.