Finite-time Differential Game for Nonlinear Systems Using Adaptive Dynamic Programming

In this paper, the finite-time differential game problem for a class of affine nonlinear system is investigated via adaptive dynamic programming(ADP). The cost function and optimal control strategy are found by solving the finite-time differential game problem via ADP technique combining a novel speed function. The single critic network is constructed to approximate the solution of associated Hamilton-Jacobi-Isaacs (HJI) equation online. The Lyapunov's direct method is utilized to demonstrate the closed-loop finite-time system and the estimation weight error of the critic network are uniformly ultimately bounded(UUB). Finally, simulation results are given to verify theoretical claims.