Numerical Approximation of Riccati-Based Hyperbolic-Like Feedback Controls

Irena Lasiecka (), Roberto Triggiani () and Xiang Wan ()
Additional contact information
Irena Lasiecka: The University of Memphis
Roberto Triggiani: The University of Memphis
Xiang Wan: Loyola University Chicago

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 15, 45 pages

Abstract: 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.

Keywords: Riccati equations; Optimal control; Finite dimensional approximation; 35L20; 35A35; 65N22 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02640-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:205:y:2025:i:2:d:10.1007_s10957-025-02640-5

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02640-5

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().