IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/1386242.html
   My bibliography  Save this article

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

Author

Listed:
  • Atamurat Kuchkarov
  • Gafurjan Ibragimov
  • Massimiliano Ferrara

Abstract

We consider pursuit and evasion differential games of a group of pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnddns:1386242
    DOI: 10.1155/2016/1386242
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2016/1386242.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2016/1386242.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/1386242?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
    ---><---

    References listed on IDEAS

    as
    1. A. A. Melikyan & N. V. Ovakimyan & L. L. Harutiunian, 1998. "Games of Simple Pursuit and Approach on a Two-Dimensional Cone," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 515-543, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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.

      More about this item

      Statistics

      Access and download statistics

      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:hin:jnddns:1386242. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.