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.
Keywords: Minimal time control, exact synchronization, minimal norm control, parabolic system
@article{COCV_2021__27_1_A44_0,
author = {Wang, Lijuan and Yan, Qishu},
title = {Minimal time control of exact synchronization for parabolic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021043},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021043/}
}
TY - JOUR AU - Wang, Lijuan AU - Yan, Qishu TI - Minimal time control of exact synchronization for parabolic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021043/ DO - 10.1051/cocv/2021043 LA - en ID - COCV_2021__27_1_A44_0 ER -
%0 Journal Article %A Wang, Lijuan %A Yan, Qishu %T Minimal time control of exact synchronization for parabolic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021043/ %R 10.1051/cocv/2021043 %G en %F COCV_2021__27_1_A44_0
Wang, Lijuan; Yan, Qishu. Minimal time control of exact synchronization for parabolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 42. doi: 10.1051/cocv/2021043
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Cité par Sources :
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.
