Stabilization of linearized Korteweg-de Vries systems with anti-diffusion by boundary feedback with non-collocated observation

Shuxia Tang, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

Abstract

This paper addresses the problem of stabilizing a class of one-dimensional linearized Korteweg-de Vries systems with possible anti-diffusion (LKdVA for short), through control at one end and non-collocated observation at the other end. An exponentially convergent observer is designed, and then a dynamical stabilizing output feedback boundary controller is constructed based on the observer. The resulting closed-loop systems can achieve arbitrary exponential decay rate. In order to derive invertibility of the kernel function in the backstepping transformation between the observer error systems and its corresponding target systems, stabilizing of a critical case of LKdVA is considered in the Appendix, which can also be treated as a preliminary problem for the main part of this paper.

Original languageEnglish
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1959-1964
Number of pages6
ISBN (Electronic)9781479986842
DOIs
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

NameProceedings of the American Control Conference
Volume2015-July
ISSN (Print)0743-1619

Conference

Conference2015 American Control Conference, ACC 2015
Country/TerritoryUnited States
CityChicago
Period07/1/1507/3/15

Keywords

  • Anti-diffusion
  • Backstepping
  • Linearized Korteweg-de Vries systems
  • Observer
  • Output feedback

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