IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v2y2014i2p68-82d35030.html
   My bibliography  Save this article

Numerical Construction of Viable Sets for Autonomous Conflict Control Systems

Author

Listed:
  • Nikolai Botkin

    (Center for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching 85747, Germany)

  • Varvara Turova

    (Center for Mathematics, Technische Universität München, Boltzmannstr. 3, Garching 85747, Germany)

Abstract

A conflict control system with state constraints is under consideration. A method for finding viability kernels (the largest subsets of state constraints where the system can be confined) is proposed. The method is related to differential games theory essentially developed by N. N. Krasovskii and A. I. Subbotin. The viability kernel is constructed as the limit of sets generated by a Pontryagin-like backward procedure. This method is implemented in the framework of a level set technique based on the computation of limiting viscosity solutions of an appropriate Hamilton–Jacobi equation. To fulfill this, the authors adapt their numerical methods formerly developed for solving time-dependent Hamilton–Jacobi equations arising from problems with state constraints. Examples of computing viability sets are given.

Suggested Citation

  • Nikolai Botkin & Varvara Turova, 2014. "Numerical Construction of Viable Sets for Autonomous Conflict Control Systems," Mathematics, MDPI, vol. 2(2), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:2:y:2014:i:2:p:68-82:d:35030
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/2/2/68/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/2/2/68/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:2:y:2014:i:2:p:68-82:d:35030. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.