Numerical Analysis of Optimality-System POD for Constrained Optimal Control

Grimm, Eva; Gubisch, Martin; Volkwein, Stefan

Numerical Analysis of Optimality-System POD for Constrained Optimal Control

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Date

2015

Publication type

Contribution to a conference collection

Publication status

Published

Published in

Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems / Mehl, Miriam et al. (ed.). - Cham [u.a.] : Springer, 2015. - (Lecture Notes in Computational Science and Engineering ; 105). - pp. 297-317. - ISSN 1439-7358. - eISSN 2197-7100. - ISBN 978-3-319-22996-6

Abstract

In this work linear-quadratic optimal control problems for parabolic equations with control and state constraints are considered. Utilizing a Lavrentiev regularization we obtain a linear-quadratic optimal control problem with mixed control-state constraints. For the numerical solution a Galerkin discretization is applied utilizing proper orthogonal decomposition (POD). Based on a perturbation method it is determined by a-posteriori error analysis how far the suboptimal control, computed on the basis of the POD method, is from the (unknown) exact one. POD basis updates are computed by optimality-system POD. Numerical examples illustrate the theoretical results for control and state constrained optimal control problems.

Subject (DDC)

510 Mathematics

Conference

3rd International Workshop on Computational Engineering (CE 2014), Oct 6, 2014 - Oct 10, 2014, Stuttgart

Cite This

ISO 690

GRIMM, Eva, Martin GUBISCH, Stefan VOLKWEIN, 2015. Numerical Analysis of Optimality-System POD for Constrained Optimal Control. 3rd International Workshop on Computational Engineering (CE 2014). Stuttgart, Oct 6, 2014 - Oct 10, 2014. In: MEHL, Miriam, ed. and others. Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems. Cham [u.a.]:Springer, pp. 297-317. ISSN 1439-7358. eISSN 2197-7100. ISBN 978-3-319-22996-6. Available under: doi: 10.1007/978-3-319-22997-3_18

BibTex

@inproceedings{Grimm2015Numer-32367,
  year={2015},
  doi={10.1007/978-3-319-22997-3_18},
  title={Numerical Analysis of Optimality-System POD for Constrained Optimal Control},
  number={105},
  isbn={978-3-319-22996-6},
  issn={1439-7358},
  publisher={Springer},
  address={Cham [u.a.]},
  series={Lecture Notes in Computational Science and Engineering},
  booktitle={Recent Trends in Computational Engineering : CE2014 ; Optimization, Uncertainty, Parallel Algorithmus, Coupled and Complex Problems},
  pages={297--317},
  editor={Mehl, Miriam},
  author={Grimm, Eva and Gubisch, Martin and Volkwein, Stefan}
}

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