Min–max adaptive dynamic programming for zero-sum differential games

Abstract

In this paper, a min–max adaptive dynamic programming approach is studied for a zero-sum differential game problem with unknown nonlinear dynamics. The unknown nonlinear dynamics is learned through the online Recurrent Neural Network (RNN). The error between the learned RNN model and the dynamics of the system is proved to converge to zero. The policy iteration algorithm is utilised to solve the Hamilton–Jacobi–Isaacs (HJI) equation associated with the differential game. Furthermore, the value function in the HJI equation is approximated through a critical Neural Network with its weights and activation functions updated online iteratively. The Uniform Ultimate Bounded stability of the closed-loop system is proved based on the Lyapunov theory. Finally, the effectiveness of the proposed solution method is demonstrated by applying it to three examples.