A Proportional-Integral-Derivative Inspired Model for Opinion Dynamics in a Trust Relationship Network

Opinion dynamics (OD) studies the members' opinion formation process to a specific issue in a group interacting environment. The existing literature seldom considers the implicit information of their opinions and neighboring members' influence during iterations. This article first proposes a method to describe the members' mental processes of changing opinions based on the support information that consists of the trust relationship among the neighboring members and the difference among the neighboring members' opinions, and this method is named the support-based method. Then, a convergence condition based on the network structure is given, and an analysis of the convergence of the model is also provided. Further, inspired by the idea of the proportional-integral-derivative (PID) controller, we propose a new method to capture the opinion changes in three areas: 1) the past cumulative performance; 2) the current performance; and 3) the future trend of the performance, and this method is named PID-inspired method. Numerical experiments are provided to validate the effectiveness of the support-based method and the PID-inspired method; specifically, the PID-inspired method has a higher-convergence rate than the support-based method.