Optimal Strategies for the Game with Two Faster 3D Pursuers and One Slower 2D Evader

A pursuit-evasion differential game with two faster pursuers in 3D space and one slower evader in a 2D plane is studied. Two pursuers, which have different speeds, attempt to cooperate to capture the evader while the evader struggles to avoid or delay the capture. Using differential games and the concept of isochron, we present a complete solution to this game and develop the optimal strategies for both the pursuers and the evader. In order to guarantee the optimality of the proposed strategies, the value function of the game is given and is further proved to be the solution of the corresponding Hamilton-Jacobi-Isaacs equation. Finally, simulations are carried out with comparisons between the proposed strategies and other typical strategies, the results of which show the optimality of the proposed strategies.