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 methods effectiveness, even for exponentially unstable systems.
| Subjects: | Optimization and Control (math.OC); Numerical Analysis (math.NA) |
| MSC classes: | 49M20, 35Q93, 49M25, 93C20, 65M15, 93A15 |
| Cite as: | arXiv:2508.16801 [math.OC] |
| (or arXiv:2508.16801v2 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2508.16801 arXiv-issued DOI via DataCite |
From: Michael Kartmann Mr. [view email]
[v1]
Fri, 22 Aug 2025 21:07:24 UTC (470 KB)
[v2]
Tue, 26 May 2026 10:01:45 UTC (615 KB)
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