The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order 2 × 2 linear hyperbolic systems. The main technical point is to show that we cannot obtain a better time. The proof combines the backstepping method with the Titchmarsh convolution theorem.
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Keywords: Hyperbolic systems, Boundary controllability, Minimal control time, Backstepping method, Titchmarsh convolution theorem
@article{COCV_2021__27_1_A98_0,
author = {Hu, Long and Olive, Guillaume},
title = {Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 {\texttimes} 2 linear hyperbolic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
number = {1},
doi = {10.1051/cocv/2021091},
language = {en},
url = {https://numdam.org/articles/10.1051/cocv/2021091/}
}
TY - JOUR AU - Hu, Long AU - Olive, Guillaume TI - Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 IS - 1 PB - EDP-Sciences UR - https://numdam.org/articles/10.1051/cocv/2021091/ DO - 10.1051/cocv/2021091 LA - en ID - COCV_2021__27_1_A98_0 ER -
%0 Journal Article %A Hu, Long %A Olive, Guillaume %T Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %N 1 %I EDP-Sciences %U https://numdam.org/articles/10.1051/cocv/2021091/ %R 10.1051/cocv/2021091 %G en %F COCV_2021__27_1_A98_0
Hu, Long; Olive, Guillaume. Null controllability and finite-time stabilization in minimal time of one-dimensional first-order 2 × 2 linear hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021) no. 1, article no. 96. doi: 10.1051/cocv/2021091
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