Adaptive Dynamic Programming for a Class of Two-player Stackelberg Differential Games

In this paper, we propose an adaptive dynamic programming algorithm based on policy iteration to solve the two-player nonlinear Stackelberg differential game. Stackelberg differential game is a hierarchical decision problem that allows the leader to choose its own optimal decision by predicting the follower’s response to its decision. In this paper, Stackelberg feedback equilibrium solution is obtained by solving the coupled partial differential equations to ensure the stability of the system. A new strategy iterative algorithm for Stackelberg differential game problem is proposed. The effectiveness of the algorithm is illustrated by an example.