Finite dimensional approximations for a class of infinite dimensional time optimal control problems

In this work, we study the numerical approximation of the solutions of a class of abstract parabolic time optimal control problems with unbounded control operator. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the optimal time...

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Bibliographic Details
Published inInternational journal of control Vol. 92; no. 1; pp. 132 - 144
Main Authors Tucsnak, Marius, Valein, Julie, Wu, Chi-Ting
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2019
Taylor & Francis Ltd
Subjects
Analysis of PDEs
Distributed parameter systems
Mathematics
Norms
numerical approximation
Optimal control
Time optimal control
optimal control
distributed parameter systems
numerical approximation AMS subject classifications 93C25
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Summary:In this work, we study the numerical approximation of the solutions of a class of abstract parabolic time optimal control problems with unbounded control operator. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the optimal time and the optimal controls of the approximate time optimal problems converge (in appropriate norms) to the optimal time and to the optimal controls of the original problem. In order to prove our main theorem, we provide a nonsmooth data error estimate for abstract parabolic systems.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1228122