A hierarchical consensus method for the approximation of the consensus state, based on clustering and spectral graph theory

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• 作者：Rita Morisi ^{rita.morisi@imtlucca.it" class="auth_mail" title="E-mail the corresponding author} ; Giorgio Gnecco ; ^{giorgio.gnecco@imtlucca.it" class="auth_mail" title="E-mail the corresponding author} ; Alberto Bemporad ^{alberto.bemporad@imtlucca.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Consensus problem ; Approximation ; Hierarchical consensus ; Clustering ; Spectral graph theory
• 刊名：Engineering Applications of Artificial Intelligence
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：56
• 期：Complete
• 页码：157-174
• 全文大小：3009 K

文摘

A hierarchical method for the approximate computation of the consensus state of a network of agents is investigated. The method is motivated theoretically by spectral graph theory arguments. In a first phase, the graph is divided into a number of subgraphs with good spectral properties, i.e., a fast convergence toward the local consensus state of each subgraph. To find the subgraphs, suitable clustering methods are used. Then, an auxiliary graph is considered, to determine the final approximation of the consensus state in the original network. A theoretical investigation is performed of cases for which the hierarchical consensus method has a better performance guarantee than the non-hierarchical one (i.e., it requires a smaller number of iterations to guarantee a desired accuracy in the approximation of the consensus state of the original network). Moreover, numerical results demonstrate the effectiveness of the hierarchical consensus method for several case studies modeling real-world networks.