| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 76 | |
| Number of page(s) | 22 | |
| DOI | https://doi.org/10.1051/cocv/2018057 | |
| Published online | 05 December 2019 | |
Parameter estimation and output feedback stabilization for the linear Korteweg-de Vries equation with disturbed boundary measurement☆
1
School of Mathematics and Systems Science, Beihang University,
Beijing
100191, PR China.
2
School of Statistics, University of International Business and Economics,
Beijing
100029, PR China.
* Corresponding author: gwei@amss.ac.cn; guowei74@126.com
Received:
12
March
2018
Accepted:
14
October
2018
This paper is concerned with the parameter estimation and boundary feedback stabilization for the linear Korteweg-de Vries equation posed on a finite interval with the boundary observation at the right end and the non-collocated control at the left end. The boundary observation suffers from some unknown disturbance. An adaptive observer is designed and the adaptive laws of the parameters are obtained by the Lyapunov method. The resulted closed-loop system is proved to be well-posed and asymptotically stable in case that the length of the interval is not critical. Moreover, it is shown that the estimated parameter converges to the unknown parameter. As a by-product, a hidden regularity result is proved.
Mathematics Subject Classification: 35B35 / 35Q53 / 93C20
Key words: Korteweg-de Vries equation / output feedback stabilization / adaptive observer / hidden regularity
© EDP Sciences, SMAI 2019
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