Tight Upper Bound for the Scrambling Constant of Uniformly Jointly Connected Directed Graphs With Application to Consensus of Multiagent Systems

In this article, we give upper bounds for the scrambling constant (SC) of the composition of general uniformly jointly connected (UJC) directed graphs. Some bounds are tight as they can be achieved by the UJC complete <inline-formula><tex-math notation="LaTeX">N</tex-math>...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 8; no. 3; pp. 1082 - 1092
Main Authors: Huang, Chao, Feng, Gang, Zhang, Hao, Yan, Huaicheng
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.09.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Consensus protocol
Control systems
Convergence
Directed graphs
Distributed algorithms/control
Eigenvalues and eigenfunctions
Graph theory
Graphs
Lower bounds
Multiagent systems
networks of autonomous agents
scrambling constant (SC)
Switches
Upper bound
Upper bounds
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:In this article, we give upper bounds for the scrambling constant (SC) of the composition of general uniformly jointly connected (UJC) directed graphs. Some bounds are tight as they can be achieved by the UJC complete <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-layer graphs. Moreover, this article establishes new and explicit connections between the upper bounds and the number of consecutive graphs needed to composite a neighbor-shared graph. Then, the upper bounds are exploited to find new lower bounds for the convergence rate of consensus protocols over UJC communication graphs. The simulation shows that consensus over UJC complete <inline-formula><tex-math notation="LaTeX">N</tex-math></inline-formula>-layer graphs may have the slowest convergence rate over all unweighted switching graphs.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2021.3074247