Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls

Abstract

We studied a simple motion differential game of two pursuers and one evader in R2. The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players.