Consensus Analysis Of Opinion Based On Multi-agent Convergence Theory In An Uncertain Environment

The convergence theory of multi-agent system is widely used in many fields,such as sensor networks,mobile robots and intelligent transportation.In addition to the above applications in the engineering field,in recent years,the application of multi-agent system in the social network of opinion dynamics has also begun to emerge.This article will study how individuals regulate information exchange methods in social networks to ultimately achieve consensus among groups.Opinion dynamics is the research on the dynamic evolution of individual opinions in social networks,and its related issues can be seen as an extension of multi-agent system.Opinion dynamics and multi-agent system have something in common.Social networks in opinion dynamics can be regarded as multi-agent system,and individuals in social networks can be regarded as agents in multi-agent system.In practical application,multi-agent system also has the influence of noise.As a special case of multi-agent system,opinion dynamics is also affected by uncertainties such as noise.Noise is divided into additive noise and multiplicative noise.As long as there is information exchange between individuals in social networks,multiplicative noise will exist.For describing situations where individuals conceal their true opinions during communication,using multiplicative noise is more appropriate compared to additive noise.Therefore,this article uses multiplicative noise to model social networks and proposes a opinion dynamics model.The consistency analysis of opinions can be based on the convergence theory of multi-agent system,which is similar to the convergence research of multi-agent system.By constructing an error system for the proposed opinion dynamics model and conducting stability analysis,we can obtain sufficient conditions to make individual opinions in the social network consistent.In response to the above issues,this article will carry out the following work:Firstly,the sufficient conditions for the convergence protocol of undirected multi-agent system to be applied to directed multi-agent system are obtained,and the effectiveness of the conclusion is verified through simulation.Secondly,aiming at the mean square consistency problem of discrete-time multi-agent system with noise,a multidimensional multi-agent system model with multiplicative noise and a onedimensional multi-agent system model are proposed.The error system network is constructed by decoupling,and the convergence protocol of the system is designed based on Riccati inequality.The effectiveness of the conclusion is verified through simulation.Thirdly,in view of the existence of noise in the field of public opinion,opinion dynamics model with random noise is proposed.The concepts of multiplicative random noise,random obstinacy factor and reception degree are considered in the model.Using research methods in the field of multi-agent system such as construction error system,sufficient conditions are obtained to enable the model to achieve consistency,and the effectiveness of the conclusion is verified through simulation.