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

被引：68

作者：

Troeltzsch, F. ^{[2
]}

Volkwein, S. ^{[1
]}

机构：

[1] Graz Univ, Inst Math & Sci Comp, A-8010 Graz, Austria

[2] Berlin Univ Technol, Inst Math, Fac Math & Nat Sci 2, D-10623 Berlin, Germany

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2009年 / 44卷 / 01期

基金：

奥地利科学基金会;

关键词：

Optimal control; Model reduction; Proper orthogonal decomposition; A-posteriori error estimates; PROPER ORTHOGONAL DECOMPOSITION; NUMERICAL APPROXIMATION; BOUNDARY CONTROL; MODEL-REDUCTION; EQUATION;

D O I：

10.1007/s10589-008-9224-3

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

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.

引用

页码：83 / 115

页数：33

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