09 20, 2023
This article investigates a two-timescale opinion dynamics model, named the concatenated Friedkin–Johnsen (FJ) model, which describes the evolution of the opinions of a group of agents over a sequence of discussion events. The topology of the underlying graph changes with the event, in the sense that the agents can participate or less to an event, and the agents are stubborn, with stubbornness that can vary from one event to the other. Concatenation refers to the fact that the final opinions of an event become initial conditions of the next event. We show that a concatenated FJ model can be represented as a time-varying product of stochastic transition matrices having a special form. Conditions are investigated under which a concatenated FJ model can achieve consensus in spite of the stubbornness. Four different sufficient conditions are obtained, mainly based on the special topological structure of our stochastic matrices.
IEEE Transactions on Automatic Control, Volume: 68, Issue: 7, July 2023.
Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
University of Chinese Academy of Sciences, Beijing, China
Group for Research on Automatic Control Engineering, Department of Engineering, University of Sannio, Benevento, Italy
Division of Automatic Control, Department of Electrical Engineering, Link？ping University, Link？ping, Sweden
Department of Control Science and Engineering, Tongji University, Shanghai, China
Australian Center for Field Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, Australia
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