Network clustering: A dynamical systems and saddle-point perspective

Mathias Bürger, Daniel Zelazo, Frank Allgöwer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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 languageEnglish
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages7825-7830
Number of pages6
DOIs
StatePublished - 2011
Externally publishedYes
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: 12 Dec 201115 Dec 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control

Conference

Conference2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/TerritoryUnited States
CityOrlando, FL
Period12/12/1115/12/11

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization

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