This paper is devoted to the stabilization for a class of uncertain linearized Ginzburg–Landau equations (GLEs). The distinguishing feature of such system is the presence of serious uncertainties which enlarge the scope of the systems whereas challenge the control problem. Therefore, certain dynamic compensation mechanisms are required to overcome the uncertainties of system. Motivated by the related literature, the original complex-valued GLEs are transformed into a class of real-valued coupled parabolic systems with serious uncertainties and distinctive characteristics. For this, two classes of identifiers respectively based on passive and swapping identifiers are first introduced to design parameter dynamic compensators. Then, by combining infinite-dimensional backstepping method with the dynamic compensators, two adaptive state-feedback controllers are constructed which guarantee all the closed-loop system states are bounded while the original system states converge to zero. A numerical example is provided to validate the effectiveness of the theoretical results.
Mots-clés : Ginzburg–Landau equations, uncertain system, identifiers, stabilization
@article{COCV_2020__26_1_A44_0,
author = {Li, Jian and Liu, Yungang},
title = {Adaptive stabilization based on passive and swapping identifiers for a class of uncertain linearized {Ginzburg{\textendash}Landau} equations},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019032},
mrnumber = {4144108},
zbl = {1453.93198},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019032/}
}
TY - JOUR AU - Li, Jian AU - Liu, Yungang TI - Adaptive stabilization based on passive and swapping identifiers for a class of uncertain linearized Ginzburg–Landau equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019032/ DO - 10.1051/cocv/2019032 LA - en ID - COCV_2020__26_1_A44_0 ER -
%0 Journal Article %A Li, Jian %A Liu, Yungang %T Adaptive stabilization based on passive and swapping identifiers for a class of uncertain linearized Ginzburg–Landau equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019032/ %R 10.1051/cocv/2019032 %G en %F COCV_2020__26_1_A44_0
Li, Jian; Liu, Yungang. Adaptive stabilization based on passive and swapping identifiers for a class of uncertain linearized Ginzburg–Landau equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 44. doi : 10.1051/cocv/2019032. http://www.numdam.org/articles/10.1051/cocv/2019032/
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This work was supported by the National Natural Science Foundations of China under Grant 61403327, 61773332, 61325016, 61873146.
