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Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space

Author

Listed:
  • Idham Arif Alias

    (Universiti Putra Malaysia)

  • Gafurjan Ibragimov

    (Universiti Putra Malaysia)

  • Askar Rakhmanov

    (Tashkent University of Information Technologies)

Abstract

We consider a simple motion evasion differential game of infinitely many evaders and infinitely many pursuers in Hilbert space $$\ell _2$$ ℓ 2 . Control functions of the players are subjected to integral constraints. If the position of an evader never coincides with the position of any pursuer, then evasion is said to be possible. Problem is to find conditions of evasion. The main result of the paper is that if either (i) the total resource of evaders is greater than that of pursuers or (ii) the total resource of evaders is equal to that of pursuers and initial positions of all the evaders are not limit points for initial positions of the pursuers, then evasion is possible. Strategies for the evaders are constructed.

Suggested Citation

  • Idham Arif Alias & Gafurjan Ibragimov & Askar Rakhmanov, 2017. "Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space," Dynamic Games and Applications, Springer, vol. 7(3), pages 347-359, September.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:3:d:10.1007_s13235-016-0196-0
    DOI: 10.1007/s13235-016-0196-0
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    References listed on IDEAS

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    1. Ibragimov, Gafurjan I. & Salimi, Mehdi & Amini, Massoud, 2012. "Evasion from many pursuers in simple motion differential game with integral constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 505-511.
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    Cited by:

    1. Gafurjan Ibragimov & Sarvinoz Kuchkarova & Risman Mat Hasim & Bruno Antonio Pansera, 2022. "Differential Game for an Infinite System of Two-Block Differential Equations," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    2. Gafurjan Ibragimov & Ruzakhon Kazimirova & Bruno Antonio Pansera, 2022. "Evasion Differential Game of Multiple Pursuers and One Evader for an Infinite System of Binary Differential Equations," Mathematics, MDPI, vol. 10(23), pages 1-8, November.

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