Optimal pursuit game of two pursuers and one evader with the Grönwall type constraints on controls

Abstract

We study a differential game of two pursuers and one evader, whose dynamics are described by linear differential equations, in $\mathbb{R}^n$. The control functions of pursuers and evader are subjected to the Grönwall type constraints. The game is said to be completed when the state of the evader coincides with the state of any pursuer. The pursuers aim to complete game as soon as possible, while the evader tries to either evade capture or prolong the time until capture. We construct optimal strategies of players and find an equation for the optimal pursuit time.