Clustering Analysis For The Several Types Of Multi-agents System

Since the 21 st century,the group behavior of multi-agent systems has been paid more and more attention by researchers.The flcoking problem in group behavior has always been a hot spot.The theoretical results are also widely used in many fields,such as public opinion control,transportation,industrial and information fusion,multi-UAV formation control,etc.There are many models for multi-agents,such as Reynolds simulation model,Kuramoto oscillator model,Vicsek model,Cucker-Smale model.The multi-cluster flocking problem is an emerging hot research problem in recent years.This paper mainly studies the bi-cluster flocking(group flocking)problem.This paper is based on the research results of previous scholars,through the establishment of mathematical models,using Matrix theory,algebraic graph theory,Lyapunov stability theory,dissipative differential inequality and finite time prior hypothesis are used to study the problem of multi-cluster flocking.The main work of this paper is as follows:The first chapter and the second chapter respectively introduce the research background,research significance,research status and development dynamics,and the required preparatory knowledge.The third chapter studies the multi-cluster problem of Cucker-Smale model with control feedback.We use Lapalace Matrix and its reduced order matrix to study the problem of multi-cluster flocking.From the case of bi-cluster flocking,we gives the control feedback condition of the multi-cluster flocking.Finally,the results are verified by numerical simulation experiments.In the fourth chapter,the group flocking model of time-delay with two topologies is studied.The necessary and sufficient conditions for the group flocking problem with time delay are given by calculating the distribution of eigenvalues.In the fifth chapter,the problem of bi-cluster flocking in the Cucker-Smale model with nonlinear coupling is studied.The nonlinear coupled Cucker-Smale model makes up for the limitations of the classical model.By designing the initial condition and using the method of finite time prior hypothesis,we proved that There is always a separation speed between groups.Then,the dissipative differential inequality is used to prove bi-flocking.Finally,the results are verified by numerical simulation experiments.In the sixth chapter,we study the problem of bi-cluster flocking in discrete Cucker-Smale model.The 2 norm analysis method of continuous model is no longer applicable.In this chapter,we use infinite norm and combine with the method of finite time prior hypothesis,get the sufficient conditions for the initial value of the discrete model.The seventh chapter summarizes the main contents of the full paper and looks forward to the future feasible work.