Model reduction for a class of nonlinear delay differential equations with time-varying delays

Nathan Van De Wouw; Wim Michiels; Bart Besselink

doi:10.1109/CDC.2015.7403231

Model reduction for a class of nonlinear delay differential equations with time-varying delays

Nathan Van De Wouw, Wim Michiels, Bart Besselink

Team Bart De Schutter

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

Abstract

In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.

Original language	English
Title of host publication	Proceedings 2015 54th IEEE Conference on Decision and Control
Editors	Y Ohta, M Sampei, A Astolfi
Place of Publication	Piscataway, NJ, USA
Publisher	IEEE
Pages	6422-6428
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7403231
Publication status	Published - 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: 15 Dec 2015 → 18 Dec 2015 Conference number: 54

Conference

Conference	54th IEEE Conference on Decision and Control, CDC 2015
Abbreviated title	CDC 2015
Country/Territory	Japan
City	Osaka
Period	15/12/15 → 18/12/15

Keywords

Asymptotic stability
Delay systems
Delays
Differential equations
Mathematical model
Reduced order systems
Stability analysis

Access to Document

10.1109/CDC.2015.7403231

Cite this

@inproceedings{aaa3920f14704a2bbfefb0de20c0c7d7,

title = "Model reduction for a class of nonlinear delay differential equations with time-varying delays",

abstract = "In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.",

keywords = "Asymptotic stability, Delay systems, Delays, Differential equations, Mathematical model, Reduced order systems, Stability analysis",

author = "{Van De Wouw}, Nathan and Wim Michiels and Bart Besselink",

year = "2015",

doi = "10.1109/CDC.2015.7403231",

language = "English",

pages = "6422--6428",

editor = "Y Ohta and M Sampei and A Astolfi",

booktitle = "Proceedings 2015 54th IEEE Conference on Decision and Control",

publisher = "IEEE",

address = "United States",

note = "54th IEEE Conference on Decision and Control, CDC 2015, CDC 2015 ; Conference date: 15-12-2015 Through 18-12-2015",

}

Van De Wouw, N, Michiels, W & Besselink, B 2015, Model reduction for a class of nonlinear delay differential equations with time-varying delays. in Y Ohta, M Sampei & A Astolfi (eds), Proceedings 2015 54th IEEE Conference on Decision and Control., 7403231, IEEE, Piscataway, NJ, USA, pp. 6422-6428, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7403231

Model reduction for a class of nonlinear delay differential equations with time-varying delays. / Van De Wouw, Nathan; Michiels, Wim; Besselink, Bart.
Proceedings 2015 54th IEEE Conference on Decision and Control. ed. / Y Ohta; M Sampei; A Astolfi. Piscataway, NJ, USA: IEEE, 2015. p. 6422-6428 7403231.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

TY - GEN

T1 - Model reduction for a class of nonlinear delay differential equations with time-varying delays

AU - Van De Wouw, Nathan

AU - Michiels, Wim

AU - Besselink, Bart

N1 - Conference code: 54

PY - 2015

Y1 - 2015

N2 - In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.

AB - In this paper, a structure-preserving model reduction approach for a class of nonlinear delay differential equations with time-varying delays is proposed. Benefits of this approach are, firstly, the fact that the delay nature of the system is preserved after reduction, secondly, that input-output stability properties are preserved and, thirdly, that a computable error bound reflecting the accuracy of the reduction is provided. These results are also applicable to large-scale linear delay differential equations with constant delays. The effectiveness of the results is evidenced by means of an illustrative example involving the nonlinear delayed dynamics of the turning process.

KW - Asymptotic stability

KW - Delay systems

KW - Delays

KW - Differential equations

KW - Mathematical model

KW - Reduced order systems

KW - Stability analysis

UR - http://www.scopus.com/inward/record.url?scp=84962019784&partnerID=8YFLogxK

U2 - 10.1109/CDC.2015.7403231

DO - 10.1109/CDC.2015.7403231

M3 - Conference contribution

AN - SCOPUS:84962019784

SP - 6422

EP - 6428

BT - Proceedings 2015 54th IEEE Conference on Decision and Control

A2 - Ohta, Y

A2 - Sampei, M

A2 - Astolfi, A

PB - IEEE

CY - Piscataway, NJ, USA

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

Y2 - 15 December 2015 through 18 December 2015

ER -

Model reduction for a class of nonlinear delay differential equations with time-varying delays

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this