Controlling opinions in Deffuant model by reconfiguring the network topology

Abstract

This paper proposes a topology reconfiguration approach for improving the rate of convergence of opinions to the opinion of a pre-specified leader for the class of convergent Deffuant models with a limited number of links. From a systems theory perspective, this problem can be viewed as a constrained stochastic nonlinear on–off control problem. Accordingly, we first propose a deterministic version of the Deffuant model and rewrite its dynamic equations to reach a set of nonlinear state-space equations where opinions are state variables and link connectivities are inputs. For that model, we then design an on–off controller based on a short-sighted predictive control strategy that dynamically changes the topology of the network by a low computational burden process. Results confirm that the proposed control strategy reaches faster convergence rates of opinions to the leader’s opinion in comparison with the well-known Erdős–Rényi structure with a similar number of links. The proposed control strategy also provides a higher rate of link connectivity for the links that are connected to the leader. Furthermore, it is observed that if the network has a fixed topology based on the obtained rate of link connectivity, it will still have a relatively rapid convergence rate which is comparable with that of a fully connected topology.