IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v197y2023i3d10.1007_s10957-023-02230-3.html
   My bibliography  Save this article

On the Problem of Pursuing Two Coordinated Evaders in Linear Recurrent Differential Games

Author

Listed:
  • Nikolay N. Petrov

    (Udmurt State University)

Abstract

In finite-dimensional Euclidean space, an analysis is made of the problem of pursuit of two evaders by a group of pursuers, which is described by a linear nonstationary system of differential equations, under the assumption that the fundamental matrix of the homogeneous system is a recurrent function. It is assumed that the evaders use the same control. The pursuers use counterstrategies based on information about the initial positions and the prehistory of the control of the evaders. The set of admissible controls is a strictly convex compact with a smooth boundary, and the goal sets are the origin of coordinates. The goal of the group of pursuers is the capture of at least one evader by two pursuers or the capture of two evaders. In terms of the initial positions and parameters of the game, a sufficient condition for capture is obtained. This study is based on the method of resolving functions, which makes it possible to obtain sufficient conditions for solvability of the problem of pursuit in some guaranteed time.

Suggested Citation

  • Nikolay N. Petrov, 2023. "On the Problem of Pursuing Two Coordinated Evaders in Linear Recurrent Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1011-1023, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02230-3
    DOI: 10.1007/s10957-023-02230-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02230-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-023-02230-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nikolay N. Petrov & Nadezhda A. Solov’eva, 2019. "Multiple Capture of Given Number of Evaders in Linear Recurrent Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 417-429, July.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Nikolay N. Petrov & Nadezhda A. Solov’eva, 2019. "Multiple Capture of Given Number of Evaders in Linear Recurrent Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 417-429, July.
    3. 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.
    4. Shmuel Y. Hayoun & Tal Shima, 2017. "A Two-on-One Linear Pursuit–Evasion Game with Bounded Controls," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 837-857, September.
    5. Meir Pachter & Eloy Garcia & David W. Casbeer, 2019. "Toward a Solution of the Active Target Defense Differential Game," Dynamic Games and Applications, Springer, vol. 9(1), pages 165-216, March.
    6. 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.
    7. Nikolai N. Petrov & Nadezhda A. Solov’eva, 2019. "Capture of Given Number of Evaders in Pontryagin’s Nonstationary Example," Dynamic Games and Applications, Springer, vol. 9(3), pages 614-627, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02230-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.