On a Closed-Loop Controller for the Coevolutionary Model of Actions and Opinions via Broadcasting Information

Abstract

We deal with controlling a complex social network in which agents have actions and opinions that coevolve, mutually influencing one another. We consider an input consisting in broadcasting information to a target set of agents with the objective of steering the population, initially at a consensus, to a different consensus. For a constant input, we derive a monotone convergence result, building on which we design an algorithm that determines whether a target set is sufficient to achieve the objective and an effective heuristic to optimize the target set. Then, we introduce a feedback control law that, using information on the state of the system, dynamically revises the target set, reducing the effort needed to achieve the objective while guaranteeing convergence to the desired consensus state.