A sliding mode observer for a linear reaction–convection–diffusion equation with disturbances

Habib Dimassi; Joseph J. Winkin; Alain Vande Wouwer

doi:10.1016/j.sysconle.2018.11.014

A sliding mode observer for a linear reaction–convection–diffusion equation with disturbances

Habib Dimassi, Joseph J. Winkin, Alain Vande Wouwer

Research output: Contribution to journal › Article › peer-review

Abstract

A sliding mode observer is designed and analyzed for a linear reaction–convection–diffusion equation subject to external disturbances. Based on a discontinuous input, the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement. An appropriate Lyapunov function is used to prove the asymptotic convergence of the observation error. The performance of the proposed observer is illustrated by some numerical simulation results.

Original language	English
Pages (from-to)	40-48
Number of pages	9
Journal	Systems and Control Letters
Volume	124
DOIs	https://doi.org/10.1016/j.sysconle.2018.11.014
Publication status	Published - 1 Feb 2019

Keywords

Distributed parameters systems
Observer design
Partial differential equations
Reaction–convection–diffusion equation
Sliding modes

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10.1016/j.sysconle.2018.11.014

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title = "A sliding mode observer for a linear reaction–convection–diffusion equation with disturbances",

abstract = "A sliding mode observer is designed and analyzed for a linear reaction–convection–diffusion equation subject to external disturbances. Based on a discontinuous input, the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement. An appropriate Lyapunov function is used to prove the asymptotic convergence of the observation error. The performance of the proposed observer is illustrated by some numerical simulation results.",

keywords = "Distributed parameters systems, Observer design, Partial differential equations, Reaction–convection–diffusion equation, Sliding modes",

author = "Habib Dimassi and Winkin, {Joseph J.} and {Vande Wouwer}, Alain",

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AU - Dimassi, Habib

AU - Winkin, Joseph J.

AU - Vande Wouwer, Alain

N1 - Funding Information: This paper presents research results of the Belgian network DYSCO (Dynamical Systems, Control and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian state, Science Policy Office (BELSPO), Belgium . The scientific responsibility rests with its authors. Publisher Copyright: © 2018 Elsevier B.V. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/2/1

Y1 - 2019/2/1

N2 - A sliding mode observer is designed and analyzed for a linear reaction–convection–diffusion equation subject to external disturbances. Based on a discontinuous input, the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement. An appropriate Lyapunov function is used to prove the asymptotic convergence of the observation error. The performance of the proposed observer is illustrated by some numerical simulation results.

AB - A sliding mode observer is designed and analyzed for a linear reaction–convection–diffusion equation subject to external disturbances. Based on a discontinuous input, the proposed observer ensures both state estimation and disturbance rejection using only one boundary measurement. An appropriate Lyapunov function is used to prove the asymptotic convergence of the observation error. The performance of the proposed observer is illustrated by some numerical simulation results.

KW - Distributed parameters systems

KW - Observer design

KW - Partial differential equations

KW - Reaction–convection–diffusion equation

KW - Sliding modes

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VL - 124

SP - 40

EP - 48

JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

A sliding mode observer for a linear reaction–convection–diffusion equation with disturbances

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Keywords

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