Volume 26, 2020
|Number of page(s)||29|
|Published online||03 September 2020|
Adaptive stabilization based on passive and swapping identifiers for a class of uncertain linearized Ginzburg–Landau equations*
School of Mathematics and Information Sciences, Yantai University,
264005, PR China.
2 School of Control Science and Engineering, Shandong University, Jinan 250061, PR China.
** Corresponding author: email@example.com
Accepted: 27 April 2019
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.
Mathematics Subject Classification: 93C20 / 93D15 / 93D21
Key words: Ginzburg–Landau equations / uncertain system / identifiers / stabilization
© EDP Sciences, SMAI 2020
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