Reaching a Consensus in a Dynamically Changing Environment: A Graphical Approach

This paper presents new graph-theoretic results appropriate to the analysis of a variety of consensus problems cast in dynamically changing environments. The concepts of rooted, strongly rooted and neighbor-shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types. The graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a Sarymsakov matrix and a rooted graph are one and the same. As an illustration of the use of the concepts developed in this paper, graph-theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied Vicsek consensus problem.

• Type: Journal
• Year: 2008
• Where: SIAMCO
• Authors: Ming Cao, A. Stephen Morse, Brian D. O. Anderson
• Keywords: Consensus Problem, Graph-theoretic, Rooted Graph, SIAMCO 2008