Fixed Duration Pursuit-Evasion Differential Game Problem With Different Constraints On Control Parametersl
Adamu, Jamilu *
Department of Mathematics, Federal University, Gashua, Nigeria.
Halliru, Amnu Sulaiman
Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
Badakaya, Abbas Ja'afaru
Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we study pursuit-evasion differential game problem in which a multiple number of pursuers pursue single evader in a Hilbert space l2. The game is described by an infinite system of 1st and nth order differential equations with the control parameters of each of the pursuer and the evader subject to integral and geometric constraints respectively. Duration of the game is fixed and denoted by the positive number ϑ. The infimum of the distance between evader and pursuers at the time ϑ is the payoff of the game. During the game, the pursuers goals is to minimize the payoff as much as possible and the evader tries to makes it as large as possible. We obtain the value of the game and constructed best strategies of the players.
Keywords: Chromosomes, Pursuer, Noctuidae, evader, Modal Number, value of the game