Abstract

The emergence of new technologies such as the Internet of things and the Cloud transforms the way we interact. Whether it be human to human interaction or human to machine interaction, the size of the networks keeps growing. As the networks get more complex nowadays with many interconnected components, it is necessary to develop distributed scalable algorithms so as to minimize the computation required in decision making in such large-scale systems. In this paper, we consider a setup where each agent in the network updates its opinion by relying on its neighbors’ opinions. The information exchange between the agents is assumed to be mutual. The cluster consensus problem is investigated for networks represented by static or time-varying graphs. Joint and integral connectivity conditions are utilized to determine the number of clusters that are formed, as the interactions among the agents evolve over time. Finally, some numerical examples are given to illustrate the theoretical results.