基于微分博弈的追逃问题最优策略设计

This paper is concerned with the design of optimal strategies for the pursuit-evasion problem with multi-attacker, multi-defender and single target based on the linear quadratic differential game. Firstly, for the case that attackers and defenders maintain their group cohesion, strategies of attackers and defenders are proposed when the target moves with a certain trajectory or the target adopts evasion policy respectively, based on communication graphs among attackers, among defenders, and between attackers and defenders. Secondly, for the case that attackers and defenders stay distributed, the maximum matching algorithm of bipartite graph is used to match attackers for defenders and the multi-attacker multi-defender pursuit-evasion problem is transformed into multi two-person zero-sum differential games, and then optimal strategies of attackers and defenders are proposed. Finally, simulation examples are provided to verify the effectiveness of the proposed strategies.