IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v25y2023i02ns0219198923500068.html
   My bibliography  Save this article

One-Sided Capture in Nonlinear Differential Games

Author

Listed:
  • K. A. Shchelchkov

    (Institute of Mathematics, Information Technologies and Physics, Udmurt State University, Universitetskaya ul. 1, Izhevsk 426034, Russia)

Abstract

A differential game described by a nonlinear system of differential equations is considered in a finite-dimensional Euclidean space. The value set of the pursuer control is a finite set. The value set of the evader control is a compact set. The purpose of the pursuer is a translation of the system in a finite time to any given neighborhood of zero. The pursuer uses a piecewise open-loop strategy constructed only by using information on the state coordinates and the velocity in the partition points of a time interval. In the past work, sufficient conditions were obtained for existence of a neighborhood of zero from which the capture occurs. The statement of the capture theorem contains such a condition that some vectors set up a positive basis. In this research, we consider the case when these vectors set up a one-sided set. For this case, sufficient conditions are obtained for existence of a set of initial position, from which the capture occurs.

Suggested Citation

  • K. A. Shchelchkov, 2023. "One-Sided Capture in Nonlinear Differential Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 25(02), pages 1-14, June.
    • Handle: RePEc:wsi:igtrxx:v:25:y:2023:i:02:n:s0219198923500068
    DOI: 10.1142/S0219198923500068
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198923500068
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198923500068?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.

    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:wsi:igtrxx:v:25:y:2023:i:02:n:s0219198923500068. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.