Adaptive Dynamic Programming for A Nonlinear Single-Pursuer Single-Evader Differential Game

This paper investigates a single-pursuer single-evader (SPSE) differential game. Unlike traditional treatments, both the dynamics of the pursuer and the evader are nonlinear which makes the linear quadratic regulation can not be applicable. To solve this problem, this paper constructs the critic neural network (NN) framework to approximate the solution of the Hamilton-Jacobi-Isaacs (HJI) equations through the adaptive dynamic programming (ADP) method. The interception condition, i.e., the stability of the system is also analyzed via the Lyapunov theorem. A numerical example is presented to illustrate that and the results show that the critic NN weights estimation error and the system are uniformly ultimately bounded (UUB), i.e., the pursuer can successfully intercept the evader.