A game problem of pursuit-evasion with nth order differential equations describing players' dynamics

Abstract

In this paper, we study a pursuit-evasion differential game problem in the Hilbert space Dynamics of countable number of pursuers and evader expressed as nth-order differential equations with geometric constraints on the control functions of the players. The game terminates at a given fixed time which is denoted by ϑ. The game's payoff is the infimum of the distances between the evader and pursuers at the time ϑ. According to the rule of the game, pursuers try to minimise the distance to the evader and the evader tries to maximises it. We found value of the game and constructed players' optimal strategies.