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Time optimal control of the heat equation with pointwise control constraints***

Published online by Cambridge University Press:  15 February 2013

Karl Kunisch  and
Lijuan Wang
Karl Kunisch
Affiliation:
Institut für Mathematik, Karl-Franzens-Universität Graz, A-8010 Graz, Austria. karl.kunisch@uni-graz.at
Lijuan Wang*
Affiliation:
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China; ljwang.math@whu.edu.cn
*
∗Corresponding author.
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Abstract

Time optimal control problems for an internally controlled heat equation with pointwise control constraints are studied. By Pontryagin’s maximum principle and properties of nontrivial solutions of the heat equation, we derive a bang-bang property for time optimal control. Using the bang-bang property and establishing certain connections between time and norm optimal control problems for the heat equation, necessary and sufficient conditions for the optimal time and the optimal control are obtained.

Keywords

Bang-bang propertytime optimal controlnorm optimal control
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 2 , April 2013 , pp. 460 - 485
Copyright
© EDP Sciences, SMAI, 2013

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Footnotes

*

Supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung under SFB 32, “Mathematical Optimization and Applications in Biomedical Sciences”.

**

This work was carried out, in part, while the author was guest-researcher at the Radon Institute, Linz, supported by the Austrian Academy of Sciences. It was also partially supported by the National Natural Science Foundation of China under Grants Nos. 10971158 and 11161130003.

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