IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v64y2016i1d10.1007_s10589-015-9809-6.html
   My bibliography  Save this article

Optimization of nonlocal time-delayed feedback controllers

Author

Listed:
  • Peter Nestler

    (Technische Universität Berlin)

  • Eckehard Schöll

    (Technische Universität Berlin)

  • Fredi Tröltzsch

    (Technische Universität Berlin)

Abstract

A class of Pyragas type nonlocal feedback controllers with time-delay is investigated for the Schlögl model. The main goal is to find an optimal kernel in the controller such that the associated solution of the controlled equation is as close as possible to a desired spatio-temporal pattern. An optimal kernel is the solution to a nonlinear optimal control problem with the kernel taken as control function. The well-posedness of the optimal control problem and necessary optimality conditions are discussed for different types of kernels. Special emphasis is laid on time-periodic functions as desired patterns. Here, the cross correlation between the state and the desired pattern is invoked to set up an associated objective functional that is to be minimized. Numerical examples are presented for the 1D Schlögl model and a class of simple step functions for the kernel.

Suggested Citation

  • Peter Nestler & Eckehard Schöll & Fredi Tröltzsch, 2016. "Optimization of nonlocal time-delayed feedback controllers," Computational Optimization and Applications, Springer, vol. 64(1), pages 265-294, May.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9809-6
    DOI: 10.1007/s10589-015-9809-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-015-9809-6
    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/s10589-015-9809-6?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. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "Erratum to: On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 187-188, September.
    2. Clemens Bachmair & Eckehard Schöll, 2014. "Nonlocal control of pulse propagation in excitable media," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(11), pages 1-10, November.
    3. Chamakuri Nagaiah & Karl Kunisch & Gernot Plank, 2011. "Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology," Computational Optimization and Applications, Springer, vol. 49(1), pages 149-178, May.
    4. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 153-185, September.
    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. Eduardo Casas & Christopher Ryll & Fredi Tröltzsch, 2018. "Optimal control of a class of reaction–diffusion systems," Computational Optimization and Applications, Springer, vol. 70(3), pages 677-707, July.
    2. Daraghmeh, Adnan & Hartmann, Carsten & Qatanani, Naji, 2019. "Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 295-307.
    3. Uzunca, M. & Karasözen, B. & Küçükseyhan, T., 2017. "Moving mesh discontinuous Galerkin methods for PDEs with traveling waves," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 9-18.
    4. Sebastian Götschel & Martin Weiser, 2015. "Lossy compression for PDE-constrained optimization: adaptive error control," Computational Optimization and Applications, Springer, vol. 62(1), pages 131-155, September.

    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:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9809-6. 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.