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AIMS Mathematics

2020, Volume 5, Issue 6: 7467-7479. doi: 10.3934/math.2020478
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Research article

On pursuit-evasion differential game problem in a Hilbert space

  • 1.
    Department of Mathematics, Federal University, Gashu'a, Nigeria
  • 2.
    Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381, Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand
  • 3.
    Department of Mathematical Sciences, Bayero University, Kano, 700231, Nigeria
  • Received: 12 July 2020 Accepted: 14 September 2020 Published: 22 September 2020

  • MSC : Primary: 91A23; Secondary: 49N75

  • We consider a pursuit-evasion differential game problem in which countably many pursuers chase one evader in the Hilbert space ${\ell_2}$ and for a fixed period of time. Dynamic of each of the pursuer is governed by first order differential equations and that of the evader by a second order differential equation. The control function for each of the player satisfies an integral constraint. The distance between the evader and the closest pursuer at the stoppage time of the game is the payoff of the game. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. We constructed optimal strategies of the players and find value of the game.

    Citation: Jamilu Adamu, Kanikar Muangchoo, Abbas Ja'afaru Badakaya, Jewaidu Rilwan. On pursuit-evasion differential game problem in a Hilbert space[J]. AIMS Mathematics, 2020, 5(6): 7467-7479. doi: 10.3934/math.2020478

    Related Papers:

  • We consider a pursuit-evasion differential game problem in which countably many pursuers chase one evader in the Hilbert space ${\ell_2}$ and for a fixed period of time. Dynamic of each of the pursuer is governed by first order differential equations and that of the evader by a second order differential equation. The control function for each of the player satisfies an integral constraint. The distance between the evader and the closest pursuer at the stoppage time of the game is the payoff of the game. The goal of the pursuers is to minimize the distance to the evader and that of the evader is the opposite. We constructed optimal strategies of the players and find value of the game.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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