  In this work we are interested in the modelling and control of opinion
dynamics spreading on a time evolving network with scale-free asymptotic degree
distribution. The mathematical model is formulated as a coupling of an opinion
alignment system with a probabilistic description of the network. The optimal
control problem aims at forcing consensus over the network, to this goal a
control strategy based on the degree of connection of each agent has been
designed. A numerical method based on a model predictive strategy is then
developed and different numerical tests are reported. The results show that in
this way it is possible to drive the overall opinion toward a desired state
even if we control only a suitable fraction of the nodes.
