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Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

Author

Listed:
  • Sergey S. Kumkov

    (Ural Federal University)

  • Stéphane Ménec

    (Airbus Group/MBDA France)

  • Valerii S. Patsko

    (Ural Federal University)

Abstract

If a pursuit game with many persons can be formalized in the framework of zero-sum differential games, then general methods can be applied to solve it. But difficulties arise connected with very high dimension of the phase vector when there are too many objects. Just due to this problem, special formulations and methods have been elaborated for conflict interaction of groups of objects. This paper is a survey of publications and results on group pursuit games.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0209-z
    DOI: 10.1007/s13235-016-0209-z
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    References listed on IDEAS

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    1. V. S. Patsko & V. L. Turova, 2001. "Level Sets Of The Value Function In Differential Games With The Homicidal Chauffeur Dynamics," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 67-112.
    2. T. Shima, 2005. "Capture Conditions in a Pursuit-Evasion Game between Players with Biproper Dynamics1," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 503-528, September.
    3. I. Shevchenko, 1997. "Successive Pursuit with a Bounded Detection Domain," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 25-48, October.
    4. Sergey Ganebny & Sergey Kumkov & Stéphane Ménec & Valerii Patsko, 2012. "Model Problem in a Line with Two Pursuers and One Evader," Dynamic Games and Applications, Springer, vol. 2(2), pages 228-257, June.
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    Cited by:

    1. 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.
    2. Olga Yufereva, 2019. "Lion and Man Game in Compact Spaces," Dynamic Games and Applications, Springer, vol. 9(1), pages 281-292, March.
    3. Valerii Patsko & Marc Quincampoix, 2019. "Preface: DGAA Special Issue on Pursuit-Evasion Games and Differential Games with Incomplete Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 569-572, September.
    4. Alexander Moll & Meir Pachter & Eloy Garcia & David Casbeer & Dejan Milutinović, 2020. "Robust Policies for a Multiple-Pursuer Single-Evader Differential Game," Dynamic Games and Applications, Springer, vol. 10(1), pages 202-221, March.
    5. 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.
    6. Alexander Moll & Meir Pachter & Zachariah Fuchs, 2023. "Pure Pursuit with an Effector," Dynamic Games and Applications, Springer, vol. 13(3), pages 961-979, September.
    7. Liudmila Kamneva, 2019. "Computation of Solvability Set for Differential Games in the Plane with Simple Motion and Non-convex Terminal Set," Dynamic Games and Applications, Springer, vol. 9(3), pages 724-750, September.
    8. Meir Pachter & Sean Coates, 2019. "The Classical Homicidal Chauffeur Game," Dynamic Games and Applications, Springer, vol. 9(3), pages 800-850, September.

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