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.