Local exponential stabilization of a coupled burgers' PDE-ODE system

Agus Hasan, Shu Xia Tang

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

1 Scopus citations

Abstract

This paper concerns the boundary stabilization problem of a coupled system consisting of the Burgers' equation and a linear ordinary differential equation (ODE). The Burgers' equation is a widely considered nonlinear partial differential equation (PDE), partially due to its low order and partially due to its structure analogous to the Navier-Stokes equation which describes fluid dynamics. The controller we employ for stabilizing this nonlinear coupled system was firstly developed from the boundary control problem of the corresponding linearized system, based on an infinite-dimensional backstepping transformation. By construction of a strict Lyapunov functional, the closed-loop nonlinear system with the backstepping controller is proved to be locally exponentially stable.

Original languageEnglish
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2479-2484
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Conference

Conference56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

Keywords

  • backstepping
  • boundary control
  • coupled PDE-ODE systems
  • nonlinear systems

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  • Cite this

    Hasan, A., & Tang, S. X. (2018). Local exponential stabilization of a coupled burgers' PDE-ODE system. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 2479-2484). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264013