On the optimal control of opinion dynamics on evolving networks

TL;DR

This paper develops a control strategy for opinion dynamics on evolving scale-free networks, enabling consensus with limited control by leveraging network degree information and model predictive methods.

Contribution

It introduces a novel control approach tailored for time-evolving networks with scale-free properties, combining opinion alignment with probabilistic network modeling.

Findings

Control can achieve consensus by manipulating a fraction of nodes.

Degree-based control strategy effectively guides opinions.

Numerical tests validate the approach's efficiency.

Abstract

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.