Balanced truncation of networked linear passive systems

Xiaodong Cheng (Corresponding author), Jacquelien M.A. Scherpen, Bart Besselink

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state–spacemodel of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.

LanguageEnglish
Pages17-25
Number of pages9
JournalAutomatica
Volume104
DOIs
StatePublished - 1 Jun 2019

Fingerprint

Multi agent systems
Synchronization
Topology

Keywords

  • Balanced truncation
  • Laplacian matrix
  • Model reduction
  • Network topology
  • Passivity

Cite this

Cheng, Xiaodong ; Scherpen, Jacquelien M.A. ; Besselink, Bart. / Balanced truncation of networked linear passive systems. In: Automatica. 2019 ; Vol. 104. pp. 17-25
@article{e82bcfa6ad9a4b89b8ba94a00e8a3d55,
title = "Balanced truncation of networked linear passive systems",
abstract = "This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state–spacemodel of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.",
keywords = "Balanced truncation, Laplacian matrix, Model reduction, Network topology, Passivity",
author = "Xiaodong Cheng and Scherpen, {Jacquelien M.A.} and Bart Besselink",
year = "2019",
month = "6",
day = "1",
doi = "10.1016/j.automatica.2019.02.045",
language = "English",
volume = "104",
pages = "17--25",
journal = "Automatica",
issn = "0005-1098",
publisher = "Agon Elsevier",

}

Balanced truncation of networked linear passive systems. / Cheng, Xiaodong (Corresponding author); Scherpen, Jacquelien M.A.; Besselink, Bart.

In: Automatica, Vol. 104, 01.06.2019, p. 17-25.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Balanced truncation of networked linear passive systems

AU - Cheng,Xiaodong

AU - Scherpen,Jacquelien M.A.

AU - Besselink,Bart

PY - 2019/6/1

Y1 - 2019/6/1

N2 - This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state–spacemodel of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.

AB - This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state–spacemodel of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example.

KW - Balanced truncation

KW - Laplacian matrix

KW - Model reduction

KW - Network topology

KW - Passivity

UR - http://www.scopus.com/inward/record.url?scp=85062569186&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2019.02.045

DO - 10.1016/j.automatica.2019.02.045

M3 - Article

VL - 104

SP - 17

EP - 25

JO - Automatica

T2 - Automatica

JF - Automatica

SN - 0005-1098

ER -

Cheng X, Scherpen JMA, Besselink B. Balanced truncation of networked linear passive systems. Automatica. 2019 Jun 1;104:17-25. Available from, DOI: 10.1016/j.automatica.2019.02.045