High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

Ania Adil; Ibrahima N'Doye; Taous Meriem Laleg-Kirati

doi:10.1109/CDC51059.2022.9992555

High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

Ania Adil^*, Ibrahima N'Doye, Taous Meriem Laleg-Kirati

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.

Original language	English (US)
Title of host publication	2022 IEEE 61st Conference on Decision and Control, CDC 2022
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	235-240
Number of pages	6
ISBN (Electronic)	9781665467612
DOIs	https://doi.org/10.1109/CDC51059.2022.9992555
State	Published - 2022
Event	61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico Duration: Dec 6 2022 → Dec 9 2022

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2022-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	61st IEEE Conference on Decision and Control, CDC 2022
Country/Territory	Mexico
City	Cancun
Period	12/6/22 → 12/9/22

Keywords

disturbance rejection
High-gain observer
nonlinear observer
nonlinear triangular systems
peaking attenuation
time-varying gain

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/CDC51059.2022.9992555

Cite this

Adil, A., N'Doye, I., & Laleg-Kirati, T. M. (2022). High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains. In 2022 IEEE 61st Conference on Decision and Control, CDC 2022 (pp. 235-240). (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC51059.2022.9992555

@inproceedings{b5e97fe0799d4278995a99e4859131a0,

title = "High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains",

abstract = "This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.",

keywords = "disturbance rejection, High-gain observer, nonlinear observer, nonlinear triangular systems, peaking attenuation, time-varying gain",

author = "Ania Adil and Ibrahima N'Doye and Laleg-Kirati, {Taous Meriem}",

note = "Funding Information: This work has been supported by the King Abdullah University of Science and Technology (KAUST), Base Research Fund (BAS/1/1627-01-01) to Taous-Meriem Laleg-Kirati. Ania Adil thanks the Direction G{\'e}n{\'e}rale de la Recherche Scientique et du D{\'e}veloppement Technologique DGRSDT/MESRS-Algeria for the financial support. Publisher Copyright: {\textcopyright} 2022 IEEE.; 61st IEEE Conference on Decision and Control, CDC 2022 ; Conference date: 06-12-2022 Through 09-12-2022",

year = "2022",

doi = "10.1109/CDC51059.2022.9992555",

language = "English (US)",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Adil, A, N'Doye, I & Laleg-Kirati, TM 2022, High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains. in 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Proceedings of the IEEE Conference on Decision and Control, vol. 2022-December, Institute of Electrical and Electronics Engineers Inc., pp. 235-240, 61st IEEE Conference on Decision and Control, CDC 2022, Cancun, Mexico, 12/6/22. https://doi.org/10.1109/CDC51059.2022.9992555

High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains. / Adil, Ania; N'Doye, Ibrahima; Laleg-Kirati, Taous Meriem.
2022 IEEE 61st Conference on Decision and Control, CDC 2022. Institute of Electrical and Electronics Engineers Inc., 2022. p. 235-240 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2022-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Adil, Ania

AU - N'Doye, Ibrahima

AU - Laleg-Kirati, Taous Meriem

N1 - Funding Information: This work has been supported by the King Abdullah University of Science and Technology (KAUST), Base Research Fund (BAS/1/1627-01-01) to Taous-Meriem Laleg-Kirati. Ania Adil thanks the Direction Générale de la Recherche Scientique et du Développement Technologique DGRSDT/MESRS-Algeria for the financial support. Publisher Copyright: © 2022 IEEE.

PY - 2022

Y1 - 2022

N2 - This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.

AB - This paper proposes a high-gain observer design for nonlinear systems with delayed output measurements using time-varying gains. The proposed observer is endowed with an exponential stability guarantee and relies on the generalization of the Halanay-type inequalities. We establish that the estimated state and the adapted gain are exponentially bounded and prevent the oscillatory response of the estimates. The time-varying gain feature limits the constant high-gain values of the standard high-gain observer design to the minimum gain required to achieve stability. Furthermore, we derive an explicit relation between the maximum bound of the delay and the maximum gain parameter by using a Lyapunov-Krasovskii functional jointly with the time-varying Halanay inequality. Finally, a comparison with the standard high-gain observer is provided through numerical simulations to demonstrate the superiority of the proposed high-gain observer in rejecting the noise and reducing the peaking phenomena.

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AN - SCOPUS:85147028288

T3 - Proceedings of the IEEE Conference on Decision and Control

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EP - 240

BT - 2022 IEEE 61st Conference on Decision and Control, CDC 2022

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 61st IEEE Conference on Decision and Control, CDC 2022

Y2 - 6 December 2022 through 9 December 2022

ER -

Adil A, N'Doye I, Laleg-Kirati TM. High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains. In 2022 IEEE 61st Conference on Decision and Control, CDC 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 235-240. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC51059.2022.9992555

High-Gain Observer Design for Nonlinear Systems with Delayed Output Measurements using Time-Varying Gains

Abstract

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Keywords

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