| 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: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
26
January
2020
Accepted:
13
April
2021
Abstract
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
The first author was supported by the National Natural Science Foundation of China under grant 11771344.
The second author was supported by the National Natural Science Foundation of China under grant 11701138 and Natural Science Foundation of Hebei Province under grant A2020202033.
© EDP Sciences, SMAI 2021
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