Finite-time convergence policies in state-dependent social networks

Abstract

This paper addresses the problem of finite-time convergence in a social network for a political party or an association, modeled as a distributed iterative system with a graph dynamics chosen to mimic how people interact. It is firstly shown that, in this setting, finite-time convergence is achieved only when nodes form a complete network, and that contacting with agents with distinct opinions reduces to a half the required interconnections. Two novel strategies are presented that enable finite-time convergence, even for the case where each node only contacts the two closest neighbors. These strategies are of prime importance, for instance, in a company environment where agents can be motivated to reach faster conclusions. The performance of the proposed policies is assessed through simulation, illustrating, in particular the finite-time convergence property.