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Grüne, Lars ; Schaller, Manuel ; Schiela, Anton:
Efficient Model Predictive Control for parabolic PDEs with goal oriented error estimation.
In: SIAM Journal on Scientific Computing.
Bd. 44
(2022)
Heft 1
.
- A471-A500.
ISSN 1095-7197
DOI: https://doi.org/10.1137/20M1356324
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Specialized Adaptive Algorithms for Model Predictive Control of PDEs GR 1569/17-1 Specialized Adaptive Algorithms for Model Predictive Control of PDEs SCHI 1379/5-1 |
|---|---|
| Projektfinanzierung: |
Deutsche Forschungsgemeinschaft |
Abstract
We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a Model Predictive Control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.
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Efficient MPC for parabolic PDEs with goal oriented error estimation. (deposited 03 Aug 2020 09:27)
- Efficient Model Predictive Control for parabolic PDEs with goal oriented error estimation. (deposited 24 Feb 2022 08:26) [Aktuelle Anzeige]