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Linear evasion differential game of one evader and several pursuers with integral constraints

Author

Listed:
  • Gafurjan Ibragimov

    (Universiti Putra Malaysia
    University Mediterranea of Reggio Calabria)

  • Massimiliano Ferrara

    (University Mediterranea of Reggio Calabria
    ICRIOS-The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship Bocconi University)

  • Marks Ruziboev

    (Leiden University)

  • Bruno Antonio Pansera

    (University Mediterranea of Reggio Calabria)

Abstract

An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:3:d:10.1007_s00182-021-00760-6
    DOI: 10.1007/s00182-021-00760-6
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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.
    2. 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.
    3. Sourabh Bhattacharya & Tamer Başar & Naira Hovakimyan, 2016. "A Visibility-Based Pursuit-Evasion Game with a Circular Obstacle," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 1071-1082, December.
    4. Sergey S. Kumkov & Stéphane Ménec & Valerii S. Patsko, 2017. "Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications," Dynamic Games and Applications, Springer, vol. 7(4), pages 609-633, December.
    5. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    6. Atamurat Kuchkarov & Gafurjan Ibragimov & Massimiliano Ferrara, 2016. "Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, August.
    7. repec:dau:papers:123456789/6046 is not listed on IDEAS
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    Cited by:

    1. 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.
    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. Marks Ruziboev & Gafurjan Ibragimov & Khudoyor Mamayusupov & Adkham Khaitmetov & Bruno Antonio Pansera, 2023. "On a Linear Differential Game in the Hilbert Space ℓ 2," Mathematics, MDPI, vol. 11(24), pages 1-9, December.
    4. 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.
    5. Gafurjan Ibragimov & Marks Ruziboev & Ibroximjon Zaynabiddinov & Bruno Antonio Pansera, 2023. "Evasion Differential Game of Multiple Pursuers and a Single Evader with Geometric Constraints in ℓ 2," Games, MDPI, vol. 14(4), pages 1-6, June.
    6. Bahrom Samatov & Gafurjan Ibragimov & Bahodirjon Juraev & Massimiliano Ferrara, 2023. "On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints," Mathematics, MDPI, vol. 11(19), pages 1-13, October.
    7. Ruzakhon Kazimirova & Gafurjan Ibragimov & Bruno Antonio Pansera & Abdulla Ibragimov, 2024. "Multi-Pursuer and One-Evader Evasion Differential Game with Integral Constraints for an Infinite System of Binary Differential Equations," Mathematics, MDPI, vol. 12(8), pages 1-10, April.

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