Zero-sum differential games for nonlinear systems using adaptive dynamic programming with input constraint

In this paper, the zero-sum differential game problem for a class of nonlinear system with input constraints is investigated via adaptive dynamic programming (ADP). A suitable non-quadratic functional is utilized to embed the control constraints into the differential game problem. Then, the Nash equilibrium solution is found by solving the constrained Hamilton-Jacobi-Isaacs (HJI) equation. The single critic network is constructed to approximate the solution of associated HJI equation online. A robustifying control term is added to the controller to eliminate the effect of residual error, leading to the asymptotically stability of the closed-loop system. Simulation results verify the effectiveness of proposed method by using a simple nonlinear system.