On the control through leadership of the Hegselmann–Krause opinion formation model

This paper deals with control strategies for the Hegselmann–Krause opinion formation model with leadership. In this system, the control mechanism is included in the leader dynamics and the feedback control functions are determined via a stabilization procedure and with a model predictive optimal control process. Correspondingly, the issues of global stabilization, controllability, and tracking are investigated. The model predictive control scheme requires to solve a sequence of open-loop optimality systems discretized by an appropriate Runge–Kutta scheme and solved by a nonlinear conjugate gradient method. Results of numerical experiments demonstrate the validity of the proposed control strategies and their ability to drive the system to attain consensus.