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Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints

Author

Listed:
  • Gafurjan Ibragimov

    (Universiti Putra Malaysia)

  • Massimiliano Ferrara

    (University Mediterranea of Reggio Calabria
    Bocconi University)

  • Atamurat Kuchkarov

    (National University of Uzbekistan)

  • Bruno Antonio Pansera

    (University Mediterranea of Reggio Calabria)

Abstract

We study a simple motion evasion differential game of many pursuers and evaders. Control functions of players are subjected to integral constraints. If the state of at least one evader does not coincide with that of any pursuer forever, then evasion is said to be possible in the game. The aim of the group of evaders is to construct their strategies so that evasion can be possible in the game and the aim of the group of pursuers is opposite. The problem is to find a sufficient condition of evasion. If the total energy of pursuers is less than or equal to that of evaders, then it is proved that evasion is possible, and moreover, evasion strategies are constructed explicitly.

Suggested Citation

  • Gafurjan Ibragimov & Massimiliano Ferrara & Atamurat Kuchkarov & Bruno Antonio Pansera, 2018. "Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints," Dynamic Games and Applications, Springer, vol. 8(2), pages 352-378, June.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0226-6
    DOI: 10.1007/s13235-017-0226-6
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    References listed on IDEAS

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    1. Nesir Huseyin & Khalik G. Guseinov & Vladimir N. Ushakov, 2015. "Approximate construction of the set of trajectories of the control system described by a Volterra integral equation," Mathematische Nachrichten, Wiley Blackwell, vol. 288(16), pages 1891-1899, November.
    2. 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 & Azamat Holboyev & Tolanbay Ibaydullaev & Bruno Antonio Pansera, 2022. "Pursuit Differential Game with Slow Pursuers on the 1-Skeleton Graph of the Icosahedron," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    2. Gafurjan Ibragimov & Yusra Salleh & Idham Arif Alias & Bruno Antonio Pansera & Massimiliano Ferrara, 2023. "Evasion from Several Pursuers in the Game with Coordinate-wise Integral Constraints," Dynamic Games and Applications, Springer, vol. 13(3), pages 819-842, September.
    3. Gafurjan Ibragimov & Massimiliano Ferrara & Marks Ruziboev & Bruno Antonio Pansera, 2021. "Linear evasion differential game of one evader and several pursuers with integral constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 729-750, September.
    4. Gafurjan Ibragimov & Ikrombek Yusupov & Massimiliano Ferrara, 2023. "Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls," Mathematics, MDPI, vol. 11(2), pages 1-10, January.

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