Bounded confidence dynamics and graph control: enforcing consensus (Q828470)

This paper studies a class of bounded confidence opinion consensus system following the line of Hegselmann-Krause model. The connections between dynamic agents are evolving as their opinions get closer when they are within a range of each other and possibly farer away otherwise. As the given dynamics, the connectivity of the original network is usually not preserved. In the paper, the authors propose a control protocol to preserve the connectivity as time goes on. Two different ways of maintaining connectivity while forcing consensus have been studied. The first strategy is called on one left behind, which imposes the rule that once agents become connected they stay connected. It is shown that under certain conditions, the initial connectivity becomes sufficient for the ultimate consensus under this control rule. The second strategy is called related on one left behind, where agent connected by a path in the network are always required to be connected by a path. Numerical simulations are provided to illustrate the results and show the convergence performance.