| Issue |
ESAIM: M2AN
Volume 60, Number 3, May-June 2026
|
|
|---|---|---|
| Page(s) | 1217 - 1246 | |
| DOI | https://doi.org/10.1051/m2an/2026029 | |
| Published online | 01 June 2026 | |
Stabilization of parabolic time-varying PDES using certified reduced-order receding horizon control
Department of Mathematics and Statistics, University of Konstanz, D-78457 Konstanz, Germany
* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
21
August
2025
Accepted:
24
March
2026
Abstract
We address the stabilization of linear, time-varying parabolic PDEs using finite-dimensional receding horizon controls (RHCs) derived from reduced-order models (ROMs). We first prove exponential stability and suboptimality of the continuous-time full-order model (FOM) RHC scheme in Hilbert spaces. A Galerkin model reduction is then introduced, along with a rigorous a posteriori error analysis for the associated finite-horizon optimal control problems. This results in a ROM-based RHC algorithm that adaptively constructs reduced-order controls, ensuring exponential stability of the FOM closed-loop state and providing computable performance bounds with respect to the infinite-horizon FOM control problem. Numerical experiments with a non-smooth cost functional involving the squared 𝓁1-norm confirm the method's effectiveness, even for exponentially unstable systems.
Mathematics Subject Classification: 49M20 / 35Q93 / 49M25 / 93C20 / 65M15 / 93A15
Key words: Receding horizon control / parabolic pdes / non-smooth objectives / reduced-order modeling / proper orthogonal decomposition / a posteriori error analysis
© The authors. Published by EDP Sciences, SMAI 2026
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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