IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v193y2022i1d10.1007_s10957-021-01991-z.html
   My bibliography  Save this article

On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control

Author

Listed:
  • Abderrahim Bouach

    (Université Mohammed Seddik Benyahia, Jijel)

  • Tahar Haddad

    (Université Mohammed Seddik Benyahia, Jijel)

  • Lionel Thibault

    (Université de Montpellier)

Abstract

We consider the Volterra integro-differential equation with a time-dependent prox-regular constraint that changes in an absolutely continuous way in time (a Volterra absolutely continuous time-dependent sweeping process). The aim of our paper is twofold. The first one is to show the solvability of the initial value problem by setting up an appropriate catching-up algorithm (full discretization). This part is a continuation of our paper (Bouach et al. in arXiv: 2102.11987. 2021) where we used a semi-discretization method. Obviously, strong solutions and convergence of full discretization scheme are desirable properties, especially for numerical simulations. Applications to non-regular electrical circuits are provided. The second aim is to establish the existence of optimal solution to an optimal control problem involving the Volterra integro-differential sweeping process.

Suggested Citation

  • Abderrahim Bouach & Tahar Haddad & Lionel Thibault, 2022. "On the Discretization of Truncated Integro-Differential Sweeping Process and Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 785-830, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01991-z
    DOI: 10.1007/s10957-021-01991-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01991-z
    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/s10957-021-01991-z?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:193:y:2022:i:1:d:10.1007_s10957-021-01991-z. 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.