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

Tel Aviv University
University of Science and Technology Beijing
Université de Toulouse

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

2 引用（Scopus）

摘要

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%.

源语言	英语
主期刊名	2020 59th IEEE Conference on Decision and Control, CDC 2020
出版商	Institute of Electrical and Electronics Engineers Inc.
页	4448-4453
页数	6
ISBN（电子版）	9781728174471
DOI	https://doi.org/10.1109/CDC42340.2020.9304502
出版状态	已出版 - 14 12月 2020
已对外发布	是
活动	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, 韩国期限: 14 12月 2020 → 18 12月 2020

出版系列

姓名	Proceedings of the IEEE Conference on Decision and Control
卷	2020-December
ISSN（印刷版）	0743-1546
ISSN（电子版）	2576-2370

会议

会议	59th IEEE Conference on Decision and Control, CDC 2020
国家/地区	韩国
市	Virtual, Jeju Island
时期	14/12/20 → 18/12/20

访问文件

10.1109/CDC42340.2020.9304502

其它文件与链接

链接到 Scopus 的出版物

引用此

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

@inproceedings{dc86a26d4bc94e57a28cd194727c8192,

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.; 59th IEEE Conference on Decision and Control, CDC 2020 ; Conference date: 14-12-2020 Through 18-12-2020",

year = "2020",

month = dec,

day = "14",

doi = "10.1109/CDC42340.2020.9304502",

language = "English",

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 = "United States",

}

Zhang, J, Kang, W, Fridman, E & Seuret, A 2020, Improved observer design for heat equation with constant measurement delay via Legendre polynomials. 在 2020 59th IEEE Conference on Decision and Control, CDC 2020., 9304502, Proceedings of the IEEE Conference on Decision and Control, 卷 2020-December, Institute of Electrical and Electronics Engineers Inc., 页码 4448-4453, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, 韩国, 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 等.
2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc., 2020. 页码 4448-4453 9304502 (Proceedings of the IEEE Conference on Decision and Control; 卷 2020-December).

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

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 - https://www.scopus.com/pages/publications/85099875520

U2 - 10.1109/CDC42340.2020.9304502

DO - 10.1109/CDC42340.2020.9304502

M3 - Conference contribution

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.

T2 - 59th IEEE Conference on Decision and Control, CDC 2020

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. 在 2020 59th IEEE Conference on Decision and Control, CDC 2020. Institute of Electrical and Electronics Engineers Inc. 2020. 页码 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

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