Publikation: Finite-Dimensional Receding Horizon Control of Linear Time-Varying Parabolic PDEs : Stability Analysis and Model-Order Reduction
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2025
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DANIILIDIS, Aris, Hrsg., Lars GRÜNE, Hrsg., Josef HAUNSCHMIED, Hrsg. und andere. Model Predictive Control : Engineering Methods for Economists. Cham: Springer, 2025, S. 55-81. Dynamic Modeling and Econometrics in Economics and Finance (DMEF). 31. ISBN 978-3-031-85255-8. Verfügbar unter: doi: 10.1007/978-3-031-85256-5_3
Zusammenfassung
This chapter deals with the stabilization of a class of linear time-varying parabolic partial differential equations employing receding horizon control (RHC). Here, RHC is finite-dimensional, i.e., it enters as a time-depending linear combination of finitely many indicator functions whose total supports cover only a small part of the spatial domain. Further, we consider the squared -norm as the control cost. This leads to a nonsmooth infinite-horizon problem which allows a stabilizing optimal control with a low number of active actuators over time. First, the stabilizability of RHC is investigated. Then, to speed up numerical computation, the data-driven model-order reduction (MOR) approaches are adequately incorporated within the RHC framework. Numerical experiments are also reported which illustrate the advantages of our MOR approaches.
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510 Mathematik
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Receding horizon control, Model-order reduction, Asymptotic stability, Optimal control, Infinite-dimensional systems, Sparse controls
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AZMI, Behzad, Jan ROHLEFF, Stefan VOLKWEIN, 2025. Finite-Dimensional Receding Horizon Control of Linear Time-Varying Parabolic PDEs : Stability Analysis and Model-Order Reduction. In: DANIILIDIS, Aris, Hrsg., Lars GRÜNE, Hrsg., Josef HAUNSCHMIED, Hrsg. und andere. Model Predictive Control : Engineering Methods for Economists. Cham: Springer, 2025, S. 55-81. Dynamic Modeling and Econometrics in Economics and Finance (DMEF). 31. ISBN 978-3-031-85255-8. Verfügbar unter: doi: 10.1007/978-3-031-85256-5_3BibTex
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title={Finite-Dimensional Receding Horizon Control of Linear Time-Varying Parabolic PDEs : Stability Analysis and Model-Order Reduction},
year={2025},
doi={10.1007/978-3-031-85256-5_3},
number={31},
isbn={978-3-031-85255-8},
address={Cham},
publisher={Springer},
series={Dynamic Modeling and Econometrics in Economics and Finance (DMEF)},
booktitle={Model Predictive Control : Engineering Methods for Economists},
pages={55--81},
editor={Daniilidis, Aris and Grüne, Lars and Haunschmied, Josef},
author={Azmi, Behzad and Rohleff, Jan and Volkwein, Stefan}
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