Robust L1 model reduction for time-delay systems

Yan Hui Li; Bin Zhou; Hui Jun Cao; Chang Hong Wang

doi:10.1109/ICMLC.2005.1527161

Robust L₁ model reduction for time-delay systems

Yan Hui Li^*
, Bin Zhou
, Hui Jun Cao
, Chang Hong Wang

^*Corresponding author for this work

School of Astronautics

Daqing Petroleum Institute
Harbin Institute of Technology

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

2 Scopus citations

Abstract

This paper investigates the problem of robust L₁ model reduction for linear continuous time-delay systems with parameter uncertainties. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is asymptotically stable and has a guaranteed L₁, performance constraint. The L₁ performance criterion is first established for time-delay systems, furthermore, the sufficient conditions for the existence of admissible reduced-order models are obtained in terms of linear matrix inequalities (LMI) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) algorithm is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by the standard numerical software. In addition, the development of delay-free reduced-order models is also presented. The efficiency of the proposed technique is demonstrated by a numerical example.

Original language	English
Title of host publication	2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005
Publisher	IEEE Computer Society
Pages	1391-1396
Number of pages	6
ISBN (Electronic)	0780390911
ISBN (Print)	078039092X, 9780780390928
DOIs	https://doi.org/10.1109/ICMLC.2005.1527161
State	Published - 2005
Event	International Conference on Machine Learning and Cybernetics, ICMLC 2005 - Guangzhou, China Duration: 18 Aug 2005 → 21 Aug 2005

Publication series

Name	2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005
Volume	3

Conference

Conference	International Conference on Machine Learning and Cybernetics, ICMLC 2005
Country/Territory	China
City	Guangzhou
Period	18/08/05 → 21/08/05

Keywords

Cone complementary linearization
LMI
Model reduction
Peak-to-peak performance
Time-delay systems

Access to Document

10.1109/ICMLC.2005.1527161

Cite this

@inproceedings{e25a86964a324df1b4f97178a345c072,

title = "Robust L1 model reduction for time-delay systems",

abstract = "This paper investigates the problem of robust L1 model reduction for linear continuous time-delay systems with parameter uncertainties. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is asymptotically stable and has a guaranteed L1, performance constraint. The L1 performance criterion is first established for time-delay systems, furthermore, the sufficient conditions for the existence of admissible reduced-order models are obtained in terms of linear matrix inequalities (LMI) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) algorithm is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by the standard numerical software. In addition, the development of delay-free reduced-order models is also presented. The efficiency of the proposed technique is demonstrated by a numerical example.",

keywords = "Cone complementary linearization, LMI, Model reduction, Peak-to-peak performance, Time-delay systems",

author = "Li, \{Yan Hui\} and Bin Zhou and Cao, \{Hui Jun\} and Wang, \{Chang Hong\}",

year = "2005",

doi = "10.1109/ICMLC.2005.1527161",

language = "英语",

isbn = "078039092X",

series = "2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005",

publisher = "IEEE Computer Society",

pages = "1391--1396",

booktitle = "2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005",

address = "美国",

note = "International Conference on Machine Learning and Cybernetics, ICMLC 2005 ; Conference date: 18-08-2005 Through 21-08-2005",

}

Li, YH, Zhou, B, Cao, HJ & Wang, CH 2005, Robust L₁ model reduction for time-delay systems. in 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005. 2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005, vol. 3, IEEE Computer Society, pp. 1391-1396, International Conference on Machine Learning and Cybernetics, ICMLC 2005, Guangzhou, China, 18/08/05. https://doi.org/10.1109/ICMLC.2005.1527161

Robust L₁ model reduction for time-delay systems. / Li, Yan Hui; Zhou, Bin; Cao, Hui Jun et al.
2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005. IEEE Computer Society, 2005. p. 1391-1396 (2005 International Conference on Machine Learning and Cybernetics, ICMLC 2005; Vol. 3).

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

TY - GEN

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AU - Li, Yan Hui

AU - Zhou, Bin

AU - Cao, Hui Jun

AU - Wang, Chang Hong

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N2 - This paper investigates the problem of robust L1 model reduction for linear continuous time-delay systems with parameter uncertainties. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is asymptotically stable and has a guaranteed L1, performance constraint. The L1 performance criterion is first established for time-delay systems, furthermore, the sufficient conditions for the existence of admissible reduced-order models are obtained in terms of linear matrix inequalities (LMI) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) algorithm is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by the standard numerical software. In addition, the development of delay-free reduced-order models is also presented. The efficiency of the proposed technique is demonstrated by a numerical example.

AB - This paper investigates the problem of robust L1 model reduction for linear continuous time-delay systems with parameter uncertainties. For a given stable system, our purpose is to construct reduced-order systems, such that the error system between the two models is asymptotically stable and has a guaranteed L1, performance constraint. The L1 performance criterion is first established for time-delay systems, furthermore, the sufficient conditions for the existence of admissible reduced-order models are obtained in terms of linear matrix inequalities (LMI) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) algorithm is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by the standard numerical software. In addition, the development of delay-free reduced-order models is also presented. The efficiency of the proposed technique is demonstrated by a numerical example.

KW - Cone complementary linearization

KW - LMI

KW - Model reduction

KW - Peak-to-peak performance

KW - Time-delay systems

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