Distributed defending strategies in target-attacker-defender game with applications to cooperative guidance

A nonzero-sum Target-Attacker-Defender game is investigated, where the target attempts to evade the attacker, the attacker aims to capture the target while evading the defenders, and the multiple defenders strive to capture the attacker while achieving the cooperation among them. A new class of cost functions segmented by the game times are developed to reflect the objectives of the respective agents. By optimizing these cost functions, the optimal strategies of the agents are derived, forming an equilibrium solution of the differential game. Furthermore, considering the communication interactions between the defenders, distributed defending strategies are derived for the defenders, where each defender’s strategy depends only on its own information and that of its connected neighbors. It is proved that the distributed strategies of the defenders, together with the optimal strategies of the target and the attacker, form an ϵ equilibrium solution of the differential game. The designed strategies are applied to a terminal guidance scenario, where a tactical missile intercepts an actively-defended target. Simulations are conducted to verify the effectiveness of the design.