Consensus Over Ergodic Stationary Graph Processes

IF 6.2 1区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

IEEE Transactions on Automatic Control Pub Date : 2010-01-01 DOI:10.1109/TAC.2009.2034054

A. Tahbaz-Salehi, A. Jadbabaie

引用次数: 232

Abstract

In this technical note, we provide a necessary and sufficient condition for convergence of consensus algorithms when the underlying graphs of the network are generated by an ergodic and stationary random process. We prove that consensus algorithms converge almost surely, if and only if, the expected graph of the network contains a directed spanning tree. Our results contain the case of independent and identically distributed graph processes as a special case. We also compute the mean and variance of the random consensus value that the algorithm converges to and provide a necessary and sufficient condition for the distribution of the consensus value to be degenerate.

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遍历平稳图过程的一致性

在这篇技术笔记中，我们提供了一个共识算法收敛的充分必要条件，当网络的底层图是由一个遍历平稳随机过程生成的。我们证明了共识算法几乎肯定收敛，当且仅当网络的期望图包含有向生成树。我们的结果包含了独立和同分布图过程的特殊情况。我们还计算了算法收敛的随机一致性值的均值和方差，为一致性值的分布退化提供了充分必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

IEEE Transactions on Automatic Control 工程技术-工程：电子与电气

CiteScore

11.30

自引率

5.90%

发文量

824

审稿时长

9 months

期刊介绍： In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered: 1) Papers: Presentation of significant research, development, or application of control concepts. 2) Technical Notes and Correspondence: Brief technical notes, comments on published areas or established control topics, corrections to papers and notes published in the Transactions. In addition, special papers (tutorials, surveys, and perspectives on the theory and applications of control systems topics) are solicited.