Optimal control strategies and target selection in multi-pursuer multi-evader differential games

This paper is concerned with a conflict that N-pursuers versus M-evaders. It is a multi-pursuer multi-evader game extended from classical differential game theory to simultaneously address target selection and multi-player pursuit-evasion. Every pursuer attempts to intercept the evader it has chosen as its target while every evader does the opposite. This is modeled as a multi-player nonzero-sum differential game under a weighted directed graph. Moreover, a novel and more practical framework, the Unique-Choice (UC) games framework, is provided. Hamilton–Jacobi–Isaacs (HJI) is used for solving the game to derive the optimal distributed control strategy for each player based on graph theory. An important but has not been extensively studied issue, target selection, is studied. Different from the former research, this paper proposes a more reasonable criterion for target selection which makes the cost of pursuers minimized. The pursuers are proven to intercept evaders successfully with the proposed optimal pursuit strategy. Several illustrative examples under two different cases are presented, and the results show that the cost of pursuers with the proposed target selection algorithm is the minimum of all results.