On the optimal control of opinion dynamics on evolving networks

Giacomo Albi, Lorenzo Pareschi, Mattia Zanella
(31/10/2015 to appear in Proceedings IFIP TC7 (2015), arXiv:1511.00145)

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.