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Evasion from many pursuers in simple motion differential game with integral constraints

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  • Ibragimov, Gafurjan I.
  • Salimi, Mehdi
  • Amini, Massoud

Abstract

We study a two dimensional evasion differential game with several pursuers and one evader with integral constraints on control functions of players. Assuming that the total resource of the pursuers does not exceed that of the evader, we solve the game by presenting explicit strategy for the evader which guarantees evasion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:505-511
    DOI: 10.1016/j.ejor.2011.11.026
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    References listed on IDEAS

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    1. Yeung, David W. K., 1998. "A class of differential games which admits a feedback solution with linear value functions," European Journal of Operational Research, Elsevier, vol. 107(3), pages 737-754, June.
    2. Byung-Wook Wie, 1995. "A differential game approach to the dynamic mixed behavior traffic network equilibrium problem," European Journal of Operational Research, Elsevier, vol. 83(1), pages 117-136, May.
    3. Erickson, Gary M., 2011. "A differential game model of the marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 211(2), pages 394-402, June.
    4. Gadi Fibich & Arieh Gavious & Oded Lowengart, 2003. "Explicit Solutions of Optimization Models and Differential Games with Nonsmooth (Asymmetric) Reference-Price Effects," Operations Research, INFORMS, vol. 51(5), pages 721-734, October.
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    Citations

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    Cited by:

    1. Mehdi Salimi & Gafurjan I. Ibragimov & Stefan Siegmund & Somayeh Sharifi, 2016. "On a Fixed Duration Pursuit Differential Game with Geometric and Integral Constraints," Dynamic Games and Applications, Springer, vol. 6(3), pages 409-425, September.
    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 & 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.
    4. Venkata Ramana Makkapati & Panagiotis Tsiotras, 2019. "Optimal Evading Strategies and Task Allocation in Multi-player Pursuit–Evasion Problems," Dynamic Games and Applications, Springer, vol. 9(4), pages 1168-1187, December.
    5. 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.
    6. 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.
    7. Wei Sun & Panagiotis Tsiotras & Anthony J. Yezzi, 2019. "Multiplayer Pursuit-Evasion Games in Three-Dimensional Flow Fields," Dynamic Games and Applications, Springer, vol. 9(4), pages 1188-1207, December.
    8. Idris Ahmed & Poom Kumam & Gafurjan Ibragimov & Jewaidu Rilwan & Wiyada Kumam, 2019. "An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    9. 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.
    10. Bekhzod Aminov & Marks Ruziboev, 2024. "Evasion Differential Games in the Space of Square Summable Sequences," Games, MDPI, vol. 15(6), pages 1-6, November.

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