Institut für Mathematik, Karl-Franzens-Universität
2 School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R. China
∗ Corresponding author.
Revised: 6 February 2012
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”.
© EDP Sciences, SMAI, 2013