Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs

Lilia Ghaffour; Matti Noack; Johann Reger; Taous Meriem Laleg-Kirati

doi:10.1016/j.ifacol.2023.10.410

Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs

Lilia Ghaffour^*, Matti Noack, Johann Reger, Taous Meriem Laleg-Kirati^*

^*Corresponding author for this work

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

2 Scopus citations

Abstract

In this paper, a non-asymptotic state estimation method for a class of nonlinear partial differential equations with general boundary conditions is presented. The method combines the modulating functions method and the Newton iterative approach. The modulating functions method is instructive to simplify the state estimation problem into solving nonlinear systems of equations, to be accomplished by Netwon's method. The performance of the proposed approach is tested through a numerical example.

Original language	English (US)
Title of host publication	IFAC-PapersOnLine
Editors	Hideaki Ishii, Yoshio Ebihara, Jun-ichi Imura, Masaki Yamakita
Publisher	Elsevier B.V.
Pages	9875-9880
Number of pages	6
Edition	2
ISBN (Electronic)	9781713872344
DOIs	https://doi.org/10.1016/j.ifacol.2023.10.410
State	Published - Jul 1 2023
Event	22nd IFAC World Congress - Yokohama, Japan Duration: Jul 9 2023 → Jul 14 2023

Publication series

Name	IFAC-PapersOnLine
Number	2
Volume	56
ISSN (Electronic)	2405-8963

Conference

Conference	22nd IFAC World Congress
Country/Territory	Japan
City	Yokohama
Period	07/9/23 → 07/14/23

Keywords

modulating functions
non-asymptotic estimation
Nonlinear partial differential equations

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1016/j.ifacol.2023.10.410

Cite this

@inproceedings{d51e995e2c194827867b8fce56e23bb2,

title = "Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs",

abstract = "In this paper, a non-asymptotic state estimation method for a class of nonlinear partial differential equations with general boundary conditions is presented. The method combines the modulating functions method and the Newton iterative approach. The modulating functions method is instructive to simplify the state estimation problem into solving nonlinear systems of equations, to be accomplished by Netwon's method. The performance of the proposed approach is tested through a numerical example.",

keywords = "modulating functions, non-asymptotic estimation, Nonlinear partial differential equations",

author = "Lilia Ghaffour and Matti Noack and Johann Reger and Laleg-Kirati, \{Taous Meriem\}",

note = "Publisher Copyright: Copyright {\textcopyright} 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/); 22nd IFAC World Congress ; Conference date: 09-07-2023 Through 14-07-2023",

year = "2023",

month = jul,

day = "1",

doi = "10.1016/j.ifacol.2023.10.410",

language = "English (US)",

series = "IFAC-PapersOnLine",

publisher = "Elsevier B.V.",

number = "2",

pages = "9875--9880",

editor = "Hideaki Ishii and Yoshio Ebihara and Jun-ichi Imura and Masaki Yamakita",

booktitle = "IFAC-PapersOnLine",

edition = "2",

}

Ghaffour, L, Noack, M, Reger, J & Laleg-Kirati, TM 2023, Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs. in H Ishii, Y Ebihara, J Imura & M Yamakita (eds), IFAC-PapersOnLine. 2 edn, IFAC-PapersOnLine, no. 2, vol. 56, Elsevier B.V., pp. 9875-9880, 22nd IFAC World Congress, Yokohama, Japan, 07/9/23. https://doi.org/10.1016/j.ifacol.2023.10.410

Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs. / Ghaffour, Lilia; Noack, Matti; Reger, Johann et al.
IFAC-PapersOnLine. ed. / Hideaki Ishii; Yoshio Ebihara; Jun-ichi Imura; Masaki Yamakita. 2. ed. Elsevier B.V., 2023. p. 9875-9880 (IFAC-PapersOnLine; Vol. 56, No. 2).

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

TY - GEN

T1 - Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs

AU - Ghaffour, Lilia

AU - Noack, Matti

AU - Reger, Johann

AU - Laleg-Kirati, Taous Meriem

PY - 2023/7/1

Y1 - 2023/7/1

N2 - In this paper, a non-asymptotic state estimation method for a class of nonlinear partial differential equations with general boundary conditions is presented. The method combines the modulating functions method and the Newton iterative approach. The modulating functions method is instructive to simplify the state estimation problem into solving nonlinear systems of equations, to be accomplished by Netwon's method. The performance of the proposed approach is tested through a numerical example.

AB - In this paper, a non-asymptotic state estimation method for a class of nonlinear partial differential equations with general boundary conditions is presented. The method combines the modulating functions method and the Newton iterative approach. The modulating functions method is instructive to simplify the state estimation problem into solving nonlinear systems of equations, to be accomplished by Netwon's method. The performance of the proposed approach is tested through a numerical example.

KW - modulating functions

KW - non-asymptotic estimation

KW - Nonlinear partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=85164027904&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2023.10.410

DO - 10.1016/j.ifacol.2023.10.410

M3 - Conference contribution

AN - SCOPUS:85164027904

T3 - IFAC-PapersOnLine

SP - 9875

EP - 9880

BT - IFAC-PapersOnLine

A2 - Ishii, Hideaki

A2 - Ebihara, Yoshio

A2 - Imura, Jun-ichi

A2 - Yamakita, Masaki

PB - Elsevier B.V.

T2 - 22nd IFAC World Congress

Y2 - 9 July 2023 through 14 July 2023

ER -

Modulating Functions Approach for Non-asymptotic State Estimation of Nonlinear PDEs

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this