Synchronization Of Nonlinear Multi-agent Systems Based On Proximity Graphs In High-dimensional Spaces

A multi-agent system is a dynamic network system composed of multiple agents connected by a network.Multi-agent systems have a wide range of physical backgrounds and engineering applications.For example,the flocking and synchronization of birds or fish schools,the formation control of multiple robots,and the cooperation of unmanned aerial vehicle(UAV)groups.The dynamics of an agent is often described by differential or difference equations and the network structure can be described by a graph.So the mathematical model of a multi-agent system is a system of differential equations or difference equations coupled each other according to the structure of a graph.The multi-agent system theory involves multiple research directions such as graph theory,differential equation theory,difference equation theory,and mathematical control theory.The main research results include the relationship between the graph and the entire dynamic behavior,the mathematical modeling and analysis of complex dynamic networks based on multi-agent systems,and the design of distributed control protocols.This thesis studies multi-agent systems in high-dimensional spaces.A mathematical model of nonlinear multi-agent systems with proximity graphs in highdimensional spaces is established,which can be used as a dynamic model of biological groups or UAVs in the realistic three-dimensional space.A sufficient condition for the collision-free synchronization in high-dimensional space is proposed.Under the condition that the initial graph is connected,it is proved that,as long as the control gain is large enough,the proximity graph can always maintain the connectedness without any collision among individual agents during the motion process and the synchronization can be achieved.Finally,some numerical simulations are given to verify the obtained theoretical results.