IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i2d10.1007_s10957-017-1120-5.html
   My bibliography  Save this article

Optimal Control of the Fokker–Planck Equation with Space-Dependent Controls

Author

Listed:
  • Arthur Fleig

    (University of Bayreuth)

  • Roberto Guglielmi

    (Dyrecta Lab)

Abstract

This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker–Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well posedness of the state equation. Under these low regularity assumptions and for a general class of objective functionals, we prove the existence of optimal controls. Moreover, for common quadratic cost functionals of tracking and terminal type, we derive the system of first-order necessary optimality conditions.

Suggested Citation

  • Arthur Fleig & Roberto Guglielmi, 2017. "Optimal Control of the Fokker–Planck Equation with Space-Dependent Controls," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 408-427, August.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:2:d:10.1007_s10957-017-1120-5
    DOI: 10.1007/s10957-017-1120-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1120-5
    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/s10957-017-1120-5?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.

    References listed on IDEAS

    as
    1. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tim Breitenbach & Alfio Borzì, 2020. "The Pontryagin maximum principle for solving Fokker–Planck optimal control problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 499-533, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Noha Almulla & Rita Ferreira & Diogo Gomes, 2017. "Two Numerical Approaches to Stationary Mean-Field Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 657-682, December.
    2. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2018. "Steering the Distribution of Agents in Mean-Field Games System," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 332-357, October.
    3. Diogo A. Gomes & Levon Nurbekyan & Mariana Prazeres, 2018. "One-Dimensional Stationary Mean-Field Games with Local Coupling," Dynamic Games and Applications, Springer, vol. 8(2), pages 315-351, June.

    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:174:y:2017:i:2:d:10.1007_s10957-017-1120-5. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.