Stabilization of an ODE-Schrödinger cascade

Beibei Ren, Jun Ming Wang, Miroslav Krstic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we consider a problem of stabilization of an ODE-Schrodinger cascade, where the interconnection between them is bi-directional at a single point. By using the backstepping approach, which uses an invertible Volterra integral transformation together with the boundary feedback to convert the unstable plant into a well-damped target system, the target system in our case is given as a PDE-ODE cascade with exponential stability at the pre-designed decay rate. Instead of one-step backstepping control, which results in difficulty in finding the kernels, we develop a two-step backstepping control design by introducing an intermediate target system and an intermediate control. The exponential stability of the closed-loop system is investigated using the Lyapunov method. A numerical simulation is provided to illustrate the effectiveness of the proposed design.

Original languageEnglish
Title of host publication2012 American Control Conference, ACC 2012
Pages4345-4350
Number of pages6
StatePublished - 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

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

Conference

Conference2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period06/27/1206/29/12

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  • Cite this

    Ren, B., Wang, J. M., & Krstic, M. (2012). Stabilization of an ODE-Schrödinger cascade. In 2012 American Control Conference, ACC 2012 (pp. 4345-4350). [6315021] (Proceedings of the American Control Conference).