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Simultaneous Multiple Capture of Rigidly Coordinated Evaders

Author

Listed:
  • Aleksandr I. Blagodatskikh

    (Udmurt State University)

  • Nikolai N. Petrov

    (Udmurt State University)

Abstract

Differential games of two players represent a very serious mathematical theory. Conflict-controlled processes with many objects (at least from one of the opposing sides) are a natural generalization of differential games of two players. Mathematical problems involving the conflict interaction between two groups of controlled objects are the most difficult to investigate. The specific nature of these problems requires new methods of research. The problem of pursuit of a group of rigidly coordinated evaders in a nonstationary conflict-controlled process with equal capabilities is examined. We say that a multiple capture in the problem of pursuit holds if a certain number of pursuers catch evaders possibly at different instants. In the nonstrict simultaneous multiple capture, there is a requirement of coinciding instants of capture. Simultaneous multiple capture means that the smallest instants of capture coincide. In this paper, sufficient and necessary conditions for simultaneous multiple capture of rigidly coordinated evaders are obtained for the case where pursuers use piecewise-program counterstrategies. Control of the pursuers which can guarantee simultaneous multiple capture not later than at a finite instant is constructed explicitly. A number of examples are considered.

Suggested Citation

  • Aleksandr I. Blagodatskikh & Nikolai N. Petrov, 2019. "Simultaneous Multiple Capture of Rigidly Coordinated Evaders," Dynamic Games and Applications, Springer, vol. 9(3), pages 594-613, September.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-019-00300-8
    DOI: 10.1007/s13235-019-00300-8
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    References listed on IDEAS

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    1. Dušan M. Stipanović & Arik Melikyan & Naira Hovakimyan, 2010. "Guaranteed Strategies For Nonlinear Multi-Player Pursuit-Evasion Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(01), pages 1-17.
    2. 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 & 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 & 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.
    3. 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.

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