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

Abstract

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.