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• W1996945182 startingPage "465" @default.
• W1996945182 abstract "The main focus of this paper is on an a-posteriori analysis for differentmodel-order strategies applied to optimal control problems governed bylinear parabolic partial differential equations. Based on a perturbationmethod it is deduced how far the suboptimal control, computed on the basisof the reduced-order model, is from the (unknown) exact one.For the model-order reduction, $mathcal H_{2,alpha}$-norm optimal modelreduction (H2), balanced truncation (BT), and proper orthogonaldecomposition (POD) are studied.The proposed approach is based on semi-discretization of the underlyingdynamics for the state and the adjoint equations as a large scale lineartime-invariant (LTI) system. This system is reduced to a lower-dimensionalone using Galerkin (POD) or Petrov-Galerkin (H2, BT) projection. The sizeof the reduced-order system is iteratively increased until the error in theoptimal control, computed with the a-posteriori error estimator, satisfiesa given accuracy. The method is illustrated with numerical tests." @default.
• W1996945182 created "2016-06-24" @default.
• W1996945182 creator A5036192555 @default.
• W1996945182 creator A5054865846 @default.
• W1996945182 date "2012-08-01" @default.
• W1996945182 modified "2023-10-14" @default.
• W1996945182 title "Model reduction techniques with a-posteriori error analysis for linear-quadratic optimal control problems" @default.
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• W1996945182 doi "https://doi.org/10.3934/naco.2012.2.465" @default.
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