IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v74y2019i3d10.1007_s10898-019-00752-7.html
   My bibliography  Save this article

Optimal control problems with states of bounded variation and hysteresis

Author

Listed:
  • Olga N. Samsonyuk

    (Matrosov Institute for System Dynamics and Control Theory of SB RAS)

  • Sergey A. Timoshin

    (Matrosov Institute for System Dynamics and Control Theory of SB RAS
    SRM University AP)

Abstract

This paper is concerned with an optimal control problem for measure-driven differential equations with rate independent hysteresis. The latter is modeled by an evolution variational inequality equivalent to the action of the play operator generalized to the case of discontinuous inputs of bounded variation. The control problem we consider is, a priori, singular in the sense that it does not have, in general, optimal solutions in the class of absolutely continuous states and Lebesgue measurable controls. Hence, we extend our problem and consider it in the class of the so-called impulsive optimal control problems. We introduce the notion of a solution for the impulsive control problem with hysteresis and establish a relationship between the solution set of the impulsive system and that of the corresponding singular system. A particular attention is paid to approximation of discontinuous solutions with bounded total variation by absolutely continuous solutions. The existence of an optimal solution to the impulsive control problem with hysteresis is proved. We also propose a variant of the so-called space-time reparametrization adapted to optimal impulsive control problems with hysteresis and discuss a method for obtaining optimality conditions for impulsive processes.

Suggested Citation

  • Olga N. Samsonyuk & Sergey A. Timoshin, 2019. "Optimal control problems with states of bounded variation and hysteresis," Journal of Global Optimization, Springer, vol. 74(3), pages 565-596, July.
  • Handle: RePEc:spr:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00752-7
    DOI: 10.1007/s10898-019-00752-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-019-00752-7
    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/s10898-019-00752-7?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:jglopt:v:74:y:2019:i:3:d:10.1007_s10898-019-00752-7. 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.