Robust multi-agent differential games for general linear systems with model uncertainties

The problem of infinite-horizon multi-agent differential games is investigated, where the process can be modeled by a set of uncertain linear dynamics. The players are divided into two teams, one of which consists of a fixed number of follower agents while the other has one leader agent. The two teams constitute the adversaries. The multi-agent differential games can be transformed into a two-player game. The dynamics of the agents are subjected to norm-bound model uncertainties. Based on quadratic stabilization techniques, a set of saddle point strategies of the game is designed to stabilize the closed-loop multi-agent system, where the weighting matrices of the cost function are properly selected. For any given cost function, by modifying the solution of the linear quadratic differential game of the nominal model, the sufficient conditions are presented such that the stabilization of the system is guaranteed and the uncertainties are compensated. It is proved that the modified solution achieves optimality. A numerical example is given to verify the effectiveness of the theoretical results.