Zero-sum differential graphical game: Optimal synchronization for heterogeneous multi-agent system with additional antagonistic input
Jiang‐Wen Xiao, Ni Yang · 2017
In this paper, the synchronization problem for heterogeneous multi-agent differential graphical game with control input and antagonistic input is considered. Due to the heterogeneous agents, the tracking error system is transformed into an extended system firstly, then the previous problem is formulated into a heterogeneous multi-agent zero-sum differential graphical game. To make the multi-agent system synchronize and reach the Nash equilibrium, the solution of coupled Hamilton-Jacobi-Issacs(HJI) equation is needed. A cooperative policy iteration(PI) algorithm is provided to solve the corresponding HJI equation iteratively. The convergence of the PI algorithm is proved to show that the iterative solution can converge to the Nash equilibrium. A simulation example verifies the effectiveness of the proposed approach.