Network clustering: A dynamical systems and saddle-point perspective

Mathias Bürger; Daniel Zelazo; Frank Allgöwer

doi:https://doi.org/10.1109/CDC.2011.6161045

Network clustering: A dynamical systems and saddle-point perspective

Mathias Bürger, Daniel Zelazo, Frank Allgöwer

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

Abstract

This paper studies a class of cooperative networks that exhibit clustering in their steady-state behavior. We consider a collection of agents with heterogeneous dynamics and a bounded interaction rule between neighboring systems. We relate the steady state-behavior of the dynamical network to a static saddle-point problem. The saddle-point description of the system allows for a precise characterization of clustering. We show that the graph forms clusters along edges that are saturated and the corresponding cluster values depend only on these edges and the objective functions of each agent. We then provide a Lyapunov stability proof connecting the steady-state behavior of the dynamic system to the solution of the static saddle-point problem.

Original language	English
Title of host publication	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages	7825-7830
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2011.6161045
State	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

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https://doi.org/10.1109/CDC.2011.6161045

Cite this

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title = "Network clustering: A dynamical systems and saddle-point perspective",

abstract = "This paper studies a class of cooperative networks that exhibit clustering in their steady-state behavior. We consider a collection of agents with heterogeneous dynamics and a bounded interaction rule between neighboring systems. We relate the steady state-behavior of the dynamical network to a static saddle-point problem. The saddle-point description of the system allows for a precise characterization of clustering. We show that the graph forms clusters along edges that are saturated and the corresponding cluster values depend only on these edges and the objective functions of each agent. We then provide a Lyapunov stability proof connecting the steady-state behavior of the dynamic system to the solution of the static saddle-point problem.",

author = "Mathias B{\"u}rger and Daniel Zelazo and Frank Allg{\"o}wer",

year = "2011",

doi = "https://doi.org/10.1109/CDC.2011.6161045",

language = "الإنجليزيّة",

isbn = "9781612848006",

series = "Proceedings of the IEEE Conference on Decision and Control",

pages = "7825--7830",

booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

}

Bürger, M, Zelazo, D & Allgöwer, F 2011, Network clustering: A dynamical systems and saddle-point perspective. in 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6161045, Proceedings of the IEEE Conference on Decision and Control, pp. 7825-7830, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6161045

Network clustering: A dynamical systems and saddle-point perspective. / Bürger, Mathias; Zelazo, Daniel; Allgöwer, Frank.
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 7825-7830 6161045 (Proceedings of the IEEE Conference on Decision and Control).

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

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T1 - Network clustering

T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

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AU - Zelazo, Daniel

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PY - 2011

Y1 - 2011

N2 - This paper studies a class of cooperative networks that exhibit clustering in their steady-state behavior. We consider a collection of agents with heterogeneous dynamics and a bounded interaction rule between neighboring systems. We relate the steady state-behavior of the dynamical network to a static saddle-point problem. The saddle-point description of the system allows for a precise characterization of clustering. We show that the graph forms clusters along edges that are saturated and the corresponding cluster values depend only on these edges and the objective functions of each agent. We then provide a Lyapunov stability proof connecting the steady-state behavior of the dynamic system to the solution of the static saddle-point problem.

AB - This paper studies a class of cooperative networks that exhibit clustering in their steady-state behavior. We consider a collection of agents with heterogeneous dynamics and a bounded interaction rule between neighboring systems. We relate the steady state-behavior of the dynamical network to a static saddle-point problem. The saddle-point description of the system allows for a precise characterization of clustering. We show that the graph forms clusters along edges that are saturated and the corresponding cluster values depend only on these edges and the objective functions of each agent. We then provide a Lyapunov stability proof connecting the steady-state behavior of the dynamic system to the solution of the static saddle-point problem.

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M3 - منشور من مؤتمر

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T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 7825

EP - 7830

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Y2 - 12 December 2011 through 15 December 2011

ER -

Network clustering: A dynamical systems and saddle-point perspective

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All Science Journal Classification (ASJC) codes

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