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Differential Games for an Infinite 2-Systems of Differential Equations

Author

Listed:
  • Muminjon Tukhtasinov

    (National University of Uzbekistan, University Street, Al-Mazar District, Tashkent 1000174, Uzbekistan
    These authors contributed equally to this work.)

  • Gafurjan Ibragimov

    (Department of Mathematics, Faculty of Science, University Putra Malaysia, Serdang 43400, Malaysia
    These authors contributed equally to this work.)

  • Sarvinoz Kuchkarova

    (National University of Uzbekistan, University Street, Al-Mazar District, Tashkent 1000174, Uzbekistan
    These authors contributed equally to this work.)

  • Risman Mat Hasim

    (Department of Mathematics, Faculty of Science, University Putra Malaysia, Serdang 43400, Malaysia)

Abstract

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l 2 . Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l 2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l 2 . The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

Suggested Citation

  • Muminjon Tukhtasinov & Gafurjan Ibragimov & Sarvinoz Kuchkarova & Risman Mat Hasim, 2021. "Differential Games for an Infinite 2-Systems of Differential Equations," Mathematics, MDPI, vol. 9(13), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1467-:d:580103
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    References listed on IDEAS

    as
    1. Mehdi Salimi & Massimiliano Ferrara, 2019. "Differential game of optimal pursuit of one evader by many pursuers," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(2), pages 481-490, June.
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