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Stabilization of Parabolic Time-Varying PDEs using Certified Reduced-Order Receding Horizon Control

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2025

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https://doi.org/10.48550/arXiv.2508.16801
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http://arxiv.org/abs/2508.16801

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Institutionen der Bundesrepublik Deutschland: 05M22VSA

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Zusammenfassung

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.

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510 Mathematik

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receding horizon control, parabolic pdes, non-smooth objectives, reduced-order modeling, proper or- thogonal decomposition, a posteriori error analysis

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ISO 690AZMI, Behzad, Michael KARTMANN, Stefan VOLKWEIN, 2025. Stabilization of Parabolic Time-Varying PDEs using Certified Reduced-Order Receding Horizon Control
BibTex
@unpublished{Azmi2025Stabi-75353,
  title={Stabilization of Parabolic Time-Varying PDEs using Certified Reduced-Order Receding Horizon Control},
  year={2025},
  doi={10.48550/arXiv.2508.16801},
  author={Azmi, Behzad and Kartmann, Michael and Volkwein, Stefan}
}
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