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POD a-posteriori error estimates for linear-quadratic optimal control problems

Article

Abstract

The main focus of this paper is on an a-posteriori analysis for the method of proper orthogonal decomposition (POD) applied to optimal control problems governed by parabolic and elliptic PDEs. Based on a perturbation method it is deduced how far the suboptimal control, computed on the basis of the POD model, is from the (unknown) exact one. Numerical examples illustrate the realization of the proposed approach for linear-quadratic problems governed by parabolic and elliptic partial differential equations.

Keywords

Optimal control Model reduction Proper orthogonal decomposition A-posteriori error estimates 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Institute of Mathematics, Faculty II—Mathematics and Natural SciencesBerlin University of TechnologyBerlinGermany
  2. 2.Institute for Mathematics and Scientific ComputingUniversity of GrazGrazAustria

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