Two-on-One Pursuit when the Pursuers Have the Same Speed as the Evader ?

摘要

A two-on-one pursuit-evasion differential game is considered. The setup is akin to Isaacs’ Two Cutters and Fugitive Ship differential game. In this paper it is however assumed that the three players have equal speeds and the two cutters/pursuers have a non-zero capture radius. The case where just one of the Pursuers is endowed with a circular capture set is also considered. The state space region where capture is guaranteed is delineated, thus providing the solution of the Game of Kind, and the players’ optimal state feedback strategies and the attendant value function are synthesized, thus providing the solution of the Game of Degree.