Arbitrary decay for boundary stabilization of Schrödinger equation subject to unknown disturbance by Lyapunov approach

This paper deals with the design of boundary control to stabilize one-dimensional Schrödinger equation with general external disturbance. The backstepping method is first applied to transform the anti-stability from the free end to the control end. A variable structure feedback stabilizing controlle...

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Bibliographic Details
Published inIFAC Journal of Systems and Control Vol. 7; p. 100033
Main Authors Kang, Wen, Guo, Bao-Zhu
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 30.03.2019
Subjects
Boundary control
Distributed parameter system
Disturbance
Lyapunov function
Schrödinger equation
Boundary control
Distributed parameter system
Schrödinger equation
Disturbance
Lyapunov function
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Summary:This paper deals with the design of boundary control to stabilize one-dimensional Schrödinger equation with general external disturbance. The backstepping method is first applied to transform the anti-stability from the free end to the control end. A variable structure feedback stabilizing controller is then designed to achieve arbitrary assigned decay rate. The Galerkin approximation scheme is used to show the existence of the solution to the closed-loop system. The exponential stability of the closed-loop system is obtained by the Lyapunov functional method. A numerical example demonstrates the efficiency of the proposed control scheme.
ISSN:2468-6018
2468-6018
DOI:10.1016/j.ifacsc.2019.100033