IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v225y2024icp1056-1071.html
   My bibliography  Save this article

A numerical scheme to solve Fokker–Planck control collective-motion problem

Author

Listed:
  • Butt, M.M.
  • Roy, S.

Abstract

A numerical scheme to solve the optimal control problem, governed by Fokker–Planck (FP) equation, is presented. In particular, a bilinear optimal control framework is considered for the evolution of the probability density function (PDF), corresponding to collective (stochastic) motion. A FP optimality system is described and a Chang–Cooper (CC) discretization scheme is employed on staggered grids to numerically solve this optimality system. This CC scheme preserves non-negativity, conservation and second-order accuracy to the PDF. Analysis of the forward time Chang–Cooper (FT-CC) scheme is provided. For the time discretization, we use the Euler first-order time differencing scheme. Furthermore, a gradient update procedure combined with a projection step is investigated to solve the optimal control problem. Numerical results validate the proposed staggered-grid FT-CC scheme for the proposed control framework in stochastic motion.

Suggested Citation

  • Butt, M.M. & Roy, S., 2024. "A numerical scheme to solve Fokker–Planck control collective-motion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 1056-1071.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:1056-1071
    DOI: 10.1016/j.matcom.2023.10.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423004317
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.10.005?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. Néstor Sepúlveda & Laurence Petitjean & Olivier Cochet & Erwan Grasland-Mongrain & Pascal Silberzan & Vincent Hakim, 2013. "Collective Cell Motion in an Epithelial Sheet Can Be Quantitatively Described by a Stochastic Interacting Particle Model," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-12, March.
    2. Butt, Muhammad Munir, 2021. "Two-level difference scheme for the two-dimensional Fokker–Planck equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 276-288.
    3. Souvik Roy & Mario Annunziato & Alfio Borzì & Christian Klingenberg, 2018. "A Fokker–Planck approach to control collective motion," Computational Optimization and Applications, Springer, vol. 69(2), pages 423-459, March.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Souvik Roy & Mario Annunziato & Alfio Borzì & Christian Klingenberg, 2018. "A Fokker–Planck approach to control collective motion," Computational Optimization and Applications, Springer, vol. 69(2), pages 423-459, March.
    3. Butt, Muhammad Munir, 2021. "Two-level difference scheme for the two-dimensional Fokker–Planck equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 276-288.
    4. Simone Göttlich & Ralf Korn & Kerstin Lux, 2019. "Optimal control of electricity input given an uncertain demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 301-328, December.
    5. Suvra Pal & Souvik Roy, 2021. "On the estimation of destructive cure rate model: A new study with exponentially weighted Poisson competing risks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 324-342, August.

    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:eee:matcom:v:225:y:2024:i:c:p:1056-1071. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.