IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i2d10.1007_s10957-025-02640-5.html
   My bibliography  Save this article

Numerical Approximation of Riccati-Based Hyperbolic-Like Feedback Controls

Author

Listed:
  • Irena Lasiecka

    (The University of Memphis
    IBS, Polish Academy of Sciences)

  • Roberto Triggiani

    (The University of Memphis)

  • Xiang Wan

    (Loyola University Chicago)

Abstract

This paper provides a (rigorous) theoretical framework for the numerical approximation of Riccati-based feedback control problems of hyperbolic-like dynamics over a finite-time horizon, with emphasis on genuine unbounded control action. Both continuous and approximation theories are illustrated by specific canonical hyperbolic-like equations with boundary control, where the abstract assumptions are actually sharp regularity properties of the hyperbolic dynamics under discussion. Assumptions are divided in two groups. A first group of dynamical assumptions (actually dynamic properties) imply some preliminary critical properties of the control problem, including the definition of the would-be Riccati operator, in terms of the original data. However, in order to guarantee that such an operator is moreover the unique solution (within a specific class) of the corresponding Differential/Integral Riccati Equation, additional smoothing assumptions on the operators defining the performance index are required. The ultimate goal is to show that the the discrete finite dimensional Riccati based feedback operator, when inserted into the original PDE dynamics, provides near optimal performance.

Suggested Citation

  • Irena Lasiecka & Roberto Triggiani & Xiang Wan, 2025. "Numerical Approximation of Riccati-Based Hyperbolic-Like Feedback Controls," Journal of Optimization Theory and Applications, Springer, vol. 205(2), pages 1-45, May.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02640-5
    DOI: 10.1007/s10957-025-02640-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02640-5
    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/s10957-025-02640-5?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. Irena Lasiecka & Roberto Triggiani, 2022. "Optimal Feedback Arising in a Third-Order Dynamics with Boundary Controls and Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 831-855, June.
    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.

      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:205:y:2025:i:2:d:10.1007_s10957-025-02640-5. 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.