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Title
Uniform convergence of the POD method and applications to optimal control.
AuthorKunisch, Karl ; Markus, Müller
Published in
Discrete and Continuous Dynamical Systems - Series A, 2015, Vol. 35, Issue 9, page 4477-4501
PublishedAmerican Institute of Mathematical Sciences, 2015
LanguageEnglish
Document typeJournal Article
Keywords (EN)Proper orthogonal decomposition / reduced order systems / Galerkin approximations / parabolic equations / optimal control
ISSN1553-5231
URNurn:nbn:at:at-ubg:3-3593 Persistent Identifier (URN)
DOI10.3934/dcds.2015.35.4477 
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 The work is publicly available
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Uniform convergence of the POD method and applications to optimal control. [1.23 mb]
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Abstract (English)

We consider proper orthogonal decomposition (POD) based Galerkin approximations to parabolic systems and establish uniform convergence with respect to forcing functions. The result is used to prove convergence of POD approximations to optimal control problems that automatically update the POD basis in order to avoid problems due to unmodeled dynamics in the POD reduced order system. A numerical example illustrates the results.

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