| Since the rise of multi-agent systems,the problem of consensus has always been a basic research in this field,and the research on consensus problem aims to enable agents to achieve state convergence under appropriate protocols.The existing studies have provided a lot of theoretical basis and analysis tools such as matrix inequality,Lyapunov equation and Riccati equation for the consensus problem of multi-agent systems,moreover,its theoretical results are widely used in intelligent transportation,unmanned aerial vehicle(UAV),social network and many other fields.In the discussion of consensus problem,numerous studies assume that the real state value of the agent can be obtained,and the control protocol designed based on the state value of the agent is adopted.However,due to the limitation of measurement conditions,the state value of agent cannot be obtained accurately in practice.How to use effective methods to obtain the real state of agents is an important research content of consensus control.In addition,the interference of various random noises on the system also affects the real state value of the agent.However,the existing analysis tools are difficult to directly solve the consensus problem of the general continuous-time systems with two kinds of noises at the same time.Therefore,it is necessary to make supplementary research on this kind of system with the help of new theoretical methods.Human society is a special multi-agent system,and opinion dynamics mainly studies the opinion evolution process of individual in society based on social network.In reality,the communication between individuals is also vulnerable to noise interference.However,the traditional modeling methods of opinion spread are still not comprehensive enough when considering random noises.How to model noises in a reasonable way and study the consensus of opinion is an important topic in this field.This thesis starts from the above problems,and the main research contents are as follows:Firstly,aiming at the problem that the real state value of the agent cannot be obtained,the observer is used to estimate the real state value,and a distributed control protocol based on the estimated state value of the agent is proposed.Through analysis and demonstration,it is proved that the system can achieve consensus under the protocol proposed in this thesis.For the formation problem of multi-agent systems,the observer-based control protocol is also proposed,and the necessary and sufficient conditions for the formability of the system are obtained.Secondly,the Parameterized Riccati equation is introduced to consider the mean-square consensus problem of continuous-time systems with two kinds of noises.By constructing the error subsystem and judging its synchronization stabilization by using the key value of the Parameterized Riccati equation,the sufficient conditions for the general continuous-time multi-agent systems to reach the mean-square consensus are given,and the necessary and sufficient conditions for the scalar system to reach the mean-square consensus are obtained.Finally,considering the problem of noise interference in the process of opinion spread,an opinion dynamics model with multiplicative noise is proposed,which is studied by using the relevant theories of the consensus problem of multi-agent systems.By constructing the error system and analyzing its mean-square stability,the sufficient conditions for the model to achieve mean-square consensus under different noises are obtained.The results obtained in this thesis have been verified by simulations,which aims to supplement the consensus theory of multi-agent systems and expand its application in opinion dynamics. |
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