Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances

Habib Dimassi, Joseph J. Winkin, Alain Vande Wouwer

    Research output: Contribution in Book/Catalog/Report/Conference proceedingConference contribution

    Abstract

    We propose a robust state estimation approach for a linear reaction-convection-diffusion equation under bounded unknown disturbances. Inspired by sliding mode theory, an adequate discontinuous input function is designed to compensate for the effect of the unknown disturbances. Based on Filippov's solutions theorem, we report the existence of generalized solutions to the estimation error system subject to the discontinuous input. Based on a Lyapunov stability analysis, we show the asymptotic convergence of the estimation error. The observer is then designed under more relaxed and realistic assumptions by replacing the discontinuous input by a continuous approximation and by using adaptive techniques to compensate for the upper bound on the bounded disturbances which are rather assumed to be unknown. Numerical simulations are performed to illustrate the effectiveness of the proposed robust estimation approach.

    Original languageEnglish
    Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages4613-4618
    Number of pages6
    Volume2018-December
    ISBN (Electronic)9781538613955
    DOIs
    Publication statusPublished - 18 Jan 2019
    Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
    Duration: 17 Dec 201819 Dec 2018

    Conference

    Conference57th IEEE Conference on Decision and Control, CDC 2018
    CountryUnited States
    CityMiami
    Period17/12/1819/12/18

    Keywords

    • Infinite dimensional systems
    • linear reaction-convection-diffusion equation
    • partial differential equations
    • robust observer design

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