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

Fingerprint

Convection-diffusion-reaction Equation
Robust Estimation
State Estimation
State estimation
Error analysis
Disturbance
Estimation Error
Unknown
Filippov Solution
Adaptive Techniques
Asymptotic Convergence
Lyapunov Stability
Generalized Solution
Sliding Mode
Observer
Stability Analysis
Computer simulation
Upper bound
Numerical Simulation
Approximation

Keywords

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

Cite this

Dimassi, H., Winkin, J. J., & Vande Wouwer, A. (2019). Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances. In 2018 IEEE Conference on Decision and Control, CDC 2018 (Vol. 2018-December, pp. 4613-4618). [8619551] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619551
Dimassi, Habib ; Winkin, Joseph J. ; Vande Wouwer, Alain. / Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances. 2018 IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December Institute of Electrical and Electronics Engineers Inc., 2019. pp. 4613-4618
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Dimassi, H, Winkin, JJ & Vande Wouwer, A 2019, Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances. in 2018 IEEE Conference on Decision and Control, CDC 2018. vol. 2018-December, 8619551, Institute of Electrical and Electronics Engineers Inc., pp. 4613-4618, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619551

Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances. / Dimassi, Habib; Winkin, Joseph J.; Vande Wouwer, Alain.

2018 IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December Institute of Electrical and Electronics Engineers Inc., 2019. p. 4613-4618 8619551.

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

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N2 - 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.

AB - 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.

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KW - linear reaction-convection-diffusion equation

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Dimassi H, Winkin JJ, Vande Wouwer A. Robust State Estimation for a Linear Reaction-Convection-Diffusion Equation under Unknown Disturbances. In 2018 IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December. Institute of Electrical and Electronics Engineers Inc. 2019. p. 4613-4618. 8619551 https://doi.org/10.1109/CDC.2018.8619551