On Laplacian spectra of parametric families of closely connected networks with application to cooperative control

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• 作者：Alla Kammerdiner ; Alexander Veremyev ; Eduardo Pasiliao
• 关键词：Supernetworks ; Parametric families of graphs ; Laplacian spectra ; Average ; consensus problem
• 刊名：Journal of Global Optimization
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：67
• 期：1-2
• 页码：187-205
• 全文大小：
• 刊物类别：Business and Economics
• 刊物主题：Optimization; Operation Research/Decision Theory; Real Functions; Computer Science, general;
• 出版者：Springer US
• ISSN：1573-2916
• 卷排序：67

文摘

In this paper, we introduce mathematical models for studying a supernetwork that is comprised of closely connected groups of subnetworks. For several related classes of such supernetworks, we explicitly derive an analytical representation of their Laplacian spectra. This work is motivated by an application of spectral graph theory in cooperative control of multi-agent networked systems. Specifically, we apply our graph-theoretic results to establish bounds on the speed of convergence and the communication time-delay for solving the average-consensus problem by a supernetwork of clusters of integrator agents.