Modeling and control of opinion dynamics in the presence of higher-order interactions

Here, we study a nonlinear model of opinion dynamics where the agents interact through a directed hypergraph. We consider the presence of an opinion leader that tries to steer the dynamics of the network towards its reference opinion. Leveraging previous results on bounded convergence on directed hypergraphs [1], we provide conditions for discriminating between alternative higher-order coupling configurations between the leader and the rest of the network. We show how such conditions can be used to reduce the opinion mismatch with the leader, and optimally control a social network organized in communities.