A game problem of pursuit-evasion with nth order differential equations describing players' dynamics. Issue 2 (3rd April 2022)

• Record Type: Journal Article
• Authors: Badakaya, Abbas Ja'afaru; Halliru, Aminu Sulaiman; Adamu, Jamilu
• Is Part Of: Journal of control and decision. Volume 9:Issue 2(2022)
• Page Start: 193
• Page End: 201
• Publication Date: 2022-04-03
• Subjects: Pursuit-evasion -- value of the game -- geometric constraints -- Hilbert space; Control theory -- Periodicals; Decision making -- Periodicals; Robotics -- Periodicals; 003.505
• DOI: 10.1080/23307706.2021.1941336
• Languages: English
• ISSNs: 2330-7706

Abstract

Abstract : In this paper, we study a pursuit-evasion differential game problem in the Hilbert space ℓ 2 . Dynamics of countable number of pursuers and evader expressed as n th-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.