Volume 27, 2021
|Number of page(s)||29|
|Published online||10 May 2021|
School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University,
430072, PR China.
2 School of Science, Hebei University of Technology, Tianjin 300400, PR China.
*** Corresponding author: email@example.com
Accepted: 13 April 2021
This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The purpose of such a problem is to find a control (from a constraint set) synchronizing components of the corresponding solution vector for the controlled system in the shortest time. In this paper, we build up a necessary and sufficient condition for the optimal time and the optimal control; we also obtain how the existence of optimal controls depends on the above mentioned two parameters.
Mathematics Subject Classification: 49K20 / 93B05 / 93B07 / 93C20
Key words: Minimal time control / exact synchronization / minimal norm control / parabolic system
© EDP Sciences, SMAI 2021
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