Krause Mean Processes Generated by Cubic Stochastic Diagonally Primitive Matrices

A multi-agent system is a system of multiple interacting entities, known as intelligent agents, who possibly have different information and/or diverging interests. The agents could be robots, humans, or human teams. Opinion dynamics is a process of individual opinions in which a group of interacting agents continuously fuse their opinions on the same issue based on established rules to reach a consensus at the final stage. Historically, the idea of reaching consensus through repeated averaging was introduced by DeGroot for a structured time-invariant and synchronous environment. Since then, consensus, which is the most ubiquitous phenomenon of multi-agent systems, has become popular in various scientific fields such as biology, physics, control engineering, and social science. To some extent, a Krause mean process is a general model of opinion sharing dynamics in which the opinions are represented by vectors. In this paper, we represent opinion sharing dynamics by means of Krause mean processes generated by diagonally primitive cubic doubly stochastic matrices, and then we establish a consensus in the multi-agent system.