Introduction to Synchronization in Nature and Physics and Cooperative Control for Multi-Agent Systems on Graphs

  • Frank L. LewisEmail author
  • Hongwei Zhang
  • Kristian Hengster-Movric
  • Abhijit Das
Part of the Communications and Control Engineering book series (CCE)


This chapter presents an overview of synchronization behavior in nature and social systems. It is seen that distributed decisions made by each agent in a group based only on the information locally available to it can result in collective synchronized motion of an overall group. The idea of a communication graph that models the information flows in a multi-agent group is introduced. Mechanisms are given by which decisions can be made locally by each agent and informed leaders can guide collective behaviors by interacting directly with only a few agents. Synchronization and collective behavior phenomena are discussed in biological systems, physics and chemistry, and engineered systems. The dependence of collective behaviors of a group on the type of information flow allowed between its agents is emphasized. Various different graph topologies are presented including random graphs, small-world networks, scale-free networks, and distance formation graphs. The early work in cooperative control systems on graphs is outlined.


Random Graph Cluster Coefficient Collective Motion Graph Topology Communication Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Frank L. Lewis
    • 1
    Email author
  • Hongwei Zhang
    • 2
  • Kristian Hengster-Movric
    • 3
  • Abhijit Das
    • 4
  1. 1.UTA Research InstituteUniversity of Texas at ArlingtonFort WorthUSA
  2. 2.School of Electrical EngineeringSouthwest Jiaotong UniversityChengduChina, People’s Republic
  3. 3.UTA Research InstituteUniversity of Texas at ArlingtonFort WorthUSA
  4. 4.Advanced Systems Engineering​Danfoss Power Solutions (US) Company​AmesUSA

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