Rapid Stabilization for a Korteweg-de Vries Equation From the Left Dirichlet Boundary Condition

Author

Cerpa, E. ; Coron, J.

Author_Institution

Dept. de Mat., Univ. Tec. Federico Santa Maria, Valparaiso, Chile

Volume

58

Issue

7

fYear

2013

fDate

Jul-13

Firstpage

1688

Lastpage

1695

Abstract

This paper deals with the stabilization problem for the Korteweg-de Vries equation posed on a bounded interval. The control acts on the left Dirichlet boundary condition. At the right end-point, Dirichlet and Neumann homogeneous boundary conditions are considered. The proposed feedback law forces the exponential decay of the system under a smallness condition on the initial data. Moreover, the decay rate can be tuned to be as large as desired. The feedback control law is designed by using the backstepping method.

Keywords

Korteweg-de Vries equation; control system synthesis; feedback; stability; Dirichlet homogeneous boundary conditions; Korteweg-de Vries equation; Neumann homogeneous boundary conditions; backstepping method; exponential decay; feedback control law; feedback law forces; left Dirichlet boundary condition; rapid stabilization problem; Backstepping; Boundary conditions; Eigenvalues and eigenfunctions; Equations; Feedback control; Kernel; Linear systems; Backstepping; Korteweg-de Vries equation; stabilization by feedback;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2013.2241479

Filename

6415996