Optimal Assignment for Multiplayer Target Defense Differential Games via Analytical Geometric Approach

This article considers a multiplayer target defense differential game (TDDG) between attacker team and defender team. The attackers aim at reaching the targets while the defenders aim at intercepting their opponents. In the 1 defender vs 1 attacker scenario, a geometric approach is proposed to explicitly obtain the optimal feedback controls of the players and the Value function of the differential game. For a multiplayer game, we propose a bipartite graph matching algorithm, utilizing the Value function, to obtain the optimal assignment. The proposed algorithm performs well in reducing the computational costs. Furthermore, we conduct several simulations to validate the optimality of the proposed method.