IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v147y2010i1d10.1007_s10957-010-9706-1.html

Some searches may not work properly. We apologize for the inconvenience.

   My bibliography  Save this article

Structure of Viability Kernels for Some Linear Differential Games

Author

Listed:
  • N. D. Botkin

    (Technische Universität München)

  • E. A. Ryazantseva

    (Ural Department of Russian Academy of Sciences)

Abstract

A convenient form of necessary and sufficient conditions of viability for differential games with linear dynamics is proposed. These conditions are utilized to construct maximal viable subsets of state constraints, viability kernels, in two illustrative two-dimensional examples. These examples demonstrate the relative simplicity of the structure of the viability kernels. It was found that the boundaries of the viability kernels consist of segments of the boundary of the state constraint and of lines defined by the first integrals of the governing equations as the players use extremal constant controls. It is conjectured that such a structure holds in high dimensional cases too.

Suggested Citation

  • N. D. Botkin & E. A. Ryazantseva, 2010. "Structure of Viability Kernels for Some Linear Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 42-57, October.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9706-1
    DOI: 10.1007/s10957-010-9706-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-010-9706-1
    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/s10957-010-9706-1?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:spr:joptap:v:147:y:2010:i:1:d:10.1007_s10957-010-9706-1. 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: 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.