Output feedback stabilization of an unstable wave equation with general corrupted boundary observation

We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 50; no. 12; pp. 3164 - 3172
Main Authors: Feng, Hongyinping, Guo, Bao-Zhu
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.12.2014
Elsevier
Subjects:
Active disturbance rejection control
Applied sciences
Asymptotic properties
Boundaries
Classical and quantum physics: mechanics and fields
Classical mechanics of continuous media: general mathematical aspects
Computer science; control theory; systems
Control system synthesis
Control systems
Control theory. Systems
Disturbances
Estimators
Exact sciences and technology
Gain
Modelling and identification
Observer
Output feedback
Output feedback stabilization
Physics
Stabilization
String equation
Wave equations
Waves and wave propagation: general mathematical aspects
String equation
Active disturbance rejection control
Observer
Output feedback stabilization
Wave equation
String theory
Closed loop
Disturbance rejection
Stabilization
Control program
Feedback regulation
Control synthesis
State space
State space method
Substructure
Modeling
Partial differential equation
Robust control
Asymptotic stability
Time varying system
Feedback
Boundary control
System identification
Output feedback
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback. By the approach, the disturbance is first estimated by a relatively independent estimator; it is then canceled in the feedback loop. As a result, the control law can be designed almost as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent, and that all subsystems in the closed-loop are asymptotically stable in the energy state space. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2014.10.016