Attack-Defense Differential Games for 3D Defenders and 2D or 3D Attackers

This paper studies attack-defense differential games for multiple 3D defenders and 2D or 3D attackers, where the attackers aim to attack a target region protected by the defenders with non-negative capture radii. Since the direct analysis of many-to-many games is difficult, the problem is decomposed into multiple many-to-one subgames. For the subgame between multiple 3D defenders and a 2D attacker, this paper presents a concept of attack region and constructs a defense winning strategy based on the attack region. Based on this strategy, it is proved that if a defense coalition can win, there are no more than two members that can guarantee this winning. The analysis is extended to 3D attackers with a lowest flight altitude constraint. Under this defense strategy, the defenders move towards an estimated interception point, and the optimality of the strategy is shown. The bipartite matching with constraints is adopted to resolve many-to-many games based on subgame outcomes. Simulations are provided to validate the theoretical results.