Application of predictive control to the Hegselmann‐Krause model

Abstract

The aim of this paper is to analyze the behavior of Hegselmann‐Krause–type models. General sufficient conditions for achieving consensus are provided. Model predictive control is applied to the Hegselmann‐Krause system in the context of time scales. Numerical simulations show that the predictive control mechanism has the ability to steer the system to attain a consensus. Moreover, faster consensus speed is observed when compared with the classical model. Finally, in the case of the discrete time scale and all agents being neighbors at the initial time, conditions guaranteeing an average consensus are given.