Differential game of multiple pursuers and one evader with integral constraints of special form

We study pursuit and evasion differential games involving multiple pursuers and a single evader with integral constraints on the control functions of the players. By definition, pursuit is completed in the game if the state of a pursuer coincides with that of the evader, and evasion is possible in the game if the state of the evader never coincides with that of any pursuer. We obtain sufficient conditions of completion of pursuit and evasion. We construct pursuit strategies and an evasion strategy in pursuit and evasion games, respectively.