| Issue |
ESAIM: COCV
Volume 19, Number 2, April-June 2013
|
|
|---|---|---|
| Page(s) | 460 - 485 | |
| DOI | https://doi.org/10.1051/cocv/2012017 | |
| Published online | 15 February 2013 | |
Time optimal control of the heat equation with pointwise control constraints*,**
1
Institut für Mathematik, Karl-Franzens-Universität
Graz, A-8010
Graz,
Austria
This email address is being protected from spambots. You need JavaScript enabled to view it.
2 School of Mathematics and Statistics,
Wuhan University, Wuhan
430072, P.R.
China
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∗ Corresponding author.
Received:
6
September
2011
Revised:
6
February
2012
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.
Mathematics Subject Classification: 35K05 / 49J20 / 49J30
Key words: Bang-bang property / time optimal control / norm optimal control
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.
© EDP Sciences, SMAI, 2013
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