| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 42 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/cocv/2021043 | |
| Published online | 10 May 2021 | |
Minimal time control of exact synchronization for parabolic systems*,**
1
School of Mathematics and Statistics, Computational Science Hubei Key Laboratory, Wuhan University,
Wuhan
430072, PR China.
2
School of Science, Hebei University of Technology,
Tianjin
300400, PR China.
*** Corresponding author: yanqishu@whu.edu.cn
Received:
26
January
2020
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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