Publikation: Optimality system POD and a-posteriori error analysis for linear-quadratic problems
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2011
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Zusammenfassung
In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD basis has bad approximation properties, a huge number of POD basis function is required to solve the reduced-order problem with the desired accuracy. To overcome this problem optimality system POD (OS-POD) is utilized, where the POD basis is chosen with respect to the optimization criteria.
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510 Mathematik
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Optimal control, model reduction, proper orthogonal decomposition, a-posteriori error estimates, optimality system POD
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VOLKWEIN, Stefan, 2011. Optimality system POD and a-posteriori error analysis for linear-quadratic problemsBibTex
@techreport{Volkwein2011Optim-15360,
year={2011},
series={Konstanzer Schriften in Mathematik},
title={Optimality system POD and a-posteriori error analysis for linear-quadratic problems},
number={291},
author={Volkwein, Stefan}
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<dcterms:abstract xml:lang="eng">In this paper an abstract linear-quadratic optimal control problem governed by an evolution equation is considered. To solve this problem numerically a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The error between the POD suboptimal control and the optimal control of the original problem is controlled by an a-posteriori error analysis. However, if the POD basis has bad approximation properties, a huge number of POD basis function is required to solve the reduced-order problem with the desired accuracy. To overcome this problem optimality system POD (OS-POD) is utilized, where the POD basis is chosen with respect to the optimization criteria.</dcterms:abstract>
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