Robust multi-agent differential games with application to cooperative guidance

Abstract

Robust multi-agent differential games and its application to cooperative guidance are investigated in this paper. The multi-agent system is modeled by general linear dynamics with norm-bound parameter uncertainties. The players in the game are divided into two teams. One team consists of a leader, and the other team consists of a fixed number of followers agents that aim to achieve leader-following consensus. The two teams constitute the adversaries of a two-player zero-sum differential game. Based on quadratic stabilization techniques, a set of saddle point strategies of the game are designed to stabilize the closed-loop multi-agent system. By modifying the optimal solution of the multi-agent differential game of the nominal model, the sufficient conditions are presented such that the stabilization of the uncertain system is guaranteed. It is proved that the modified solution achieves quasi-optimality. It is also shown that L2-bounded consensus error can be achieved, if the control of the leader deviates from its quasi-optimal strategy. The model of cooperative guidance problem is established, based on which the robust multi-agent differential games approach is applied to design the cooperative guidance laws. Numerical examples are given to verify the effectiveness of the theoretical results and the performance of the proposed cooperative guidance law.