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bang-bang property

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Time optimal control of the heat equation with pointwisecontrol constraints ***
Karl Kunisch, Lijuan Wang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 2 / April 2013

Published online by Cambridge University Press:

15 February 2013, pp. 460-485

Print publication:

April 2013
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Time optimal control problems for an internally controlled heat equation with pointwisecontrol constraints are studied. By Pontryagin’s maximum principle and properties ofnontrivial solutions of the heat equation, we derive a bang-bang property for time optimalcontrol. Using the bang-bang property and establishing certain connections between timeand norm optimal control problems for the heat equation, necessary and sufficientconditions for the optimal time and the optimal control are obtained.