Improved observer design for heat equation with constant measurement delay via Legendre polynomials

Jin Zhang; Wen Kang; Emilia Fridman; Alexandre Seuret

doi:10.1109/CDC42340.2020.9304502

Improved observer design for heat equation with constant measurement delay via Legendre polynomials

Jin Zhang, Wen Kang, Emilia Fridman, Alexandre Seuret

School of Electrical Engineering

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

Abstract

In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.

Original language	English
Title of host publication	2020 59th IEEE Conference on Decision and Control, CDC 2020
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4448-4453
Number of pages	6
ISBN (Electronic)	9781728174471
DOIs	https://doi.org/10.1109/CDC42340.2020.9304502
State	Published - 14 Dec 2020
Event	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2020-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	59th IEEE Conference on Decision and Control, CDC 2020
Country/Territory	Korea, Republic of
City	Virtual, Jeju Island
Period	14/12/20 → 18/12/20

Access to Document

10.1109/CDC42340.2020.9304502

Cite this

Zhang, J., Kang, W., Fridman, E., & Seuret, A. (2020). Improved observer design for heat equation with constant measurement delay via Legendre polynomials. In 2020 59th IEEE Conference on Decision and Control, CDC 2020 (pp. 4448-4453). [9304502] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC42340.2020.9304502

@inproceedings{c22f8bd4c41540ee8abd6a4860daceb4,

title = "Improved observer design for heat equation with constant measurement delay via Legendre polynomials",

abstract = "In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.",

author = "Jin Zhang and Wen Kang and Emilia Fridman and Alexandre Seuret",

note = "Publisher Copyright: {\textcopyright} 2020 IEEE.; null ; Conference date: 14-12-2020 Through 18-12-2020",

year = "2020",

month = dec,

day = "14",

doi = "10.1109/CDC42340.2020.9304502",

language = "אנגלית",

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

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "4448--4453",

booktitle = "2020 59th IEEE Conference on Decision and Control, CDC 2020",

address = "ארצות הברית",

}

Zhang, J, Kang, W, Fridman, E & Seuret, A 2020, Improved observer design for heat equation with constant measurement delay via Legendre polynomials. in 2020 59th IEEE Conference on Decision and Control, CDC 2020., 9304502, Proceedings of the IEEE Conference on Decision and Control, vol. 2020-December, Institute of Electrical and Electronics Engineers Inc., pp. 4448-4453, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, Korea, Republic of, 14/12/20. https://doi.org/10.1109/CDC42340.2020.9304502

Improved observer design for heat equation with constant measurement delay via Legendre polynomials. / Zhang, Jin; Kang, Wen; Fridman, Emilia et al.

2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. p. 4448-4453 9304502 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).

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

TY - GEN

T1 - Improved observer design for heat equation with constant measurement delay via Legendre polynomials

AU - Zhang, Jin

AU - Kang, Wen

AU - Fridman, Emilia

AU - Seuret, Alexandre

PY - 2020/12/14

Y1 - 2020/12/14

N2 - In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.

AB - In this paper, we present improved results on observer design for 1D heat equation. We first introduce an observer under delayed spatially point measurements that leads to an estimation error with time-delay. Inspired by recent developments in the area of delayed ODEs, we suggest augmented Lyapunov functionals based on the Legendre polynomials. Then, sufficient exponential stability conditions are derived in the form of linear matrix inequalities (LMIs) that are parameterized by the degree of the polynomials. Finally, a numerical example illustrates the efficiency of the results that allow to enlarge the value of delay preserving the stability by more than 20%.

UR - http://www.scopus.com/inward/record.url?scp=85099875520&partnerID=8YFLogxK

U2 - 10.1109/CDC42340.2020.9304502

DO - 10.1109/CDC42340.2020.9304502

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85099875520

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4448

EP - 4453

BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 14 December 2020 through 18 December 2020

ER -

Zhang J, Kang W, Fridman E, Seuret A. Improved observer design for heat equation with constant measurement delay via Legendre polynomials. In 2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. p. 4448-4453. 9304502. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC42340.2020.9304502

Improved observer design for heat equation with constant measurement delay via Legendre polynomials

Abstract

Publication series

Conference

Access to Document

Other files and links

Fingerprint

Cite this