New unknown input observer and output feedback stabilization for uncertain heat equation

In this paper, we propose a new method, by designing an unknown input type state observer, to stabilize an unstable 1-d heat equation with boundary uncertainty and external disturbance. The state observer is designed in terms of a disturbance estimator. A stabilizing state feedback control is design...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 86; pp. 1 - 10
Main Authors Feng, Hongyinping, Guo, Bao-Zhu
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2017
Subjects
Disturbance
Heat equation
Nonlinear boundary
Observer
Stabilization
Heat equation
Stabilization
Observer
Disturbance
Nonlinear boundary
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Summary:In this paper, we propose a new method, by designing an unknown input type state observer, to stabilize an unstable 1-d heat equation with boundary uncertainty and external disturbance. The state observer is designed in terms of a disturbance estimator. A stabilizing state feedback control is designed for the observer by the backstepping transformation, which is an observer based output feedback stabilizing control for the original system. The well-posedness and stability of the closed-loop system are concluded. The numerical simulations show that the proposed scheme is quite effectively. This is a first result on active disturbance rejection control for a PDE with both boundary uncertainty and external disturbance.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2017.08.004