Pride of Lions and Man Differential Game

A reach-avoid differential game with multiple players is considered in this paper. A group of defenders is in charge of capturing a spy before it leaves the game set. This paper addresses cooperation among the defenders which protect a circular area of interest and try to intercept an intelligent adversary/intruder. The optimal strategies for each team, the defender team and the spy, are obtained. These strategies and the Value function are obtained in analytical and explicit form. Furthermore, it is verified that the Value function is continuously differentiable and it is the solution of the Hamilton-Jacobi-Isaacs equation. Finally, the Barrier surface that separates the winning regions of each team is obtained in explicit form. Illustrative examples show the Barrier surface cross-sections of this high dimensional differential game.