A Necessary and Sufficient Condition of an Interfering Reverse Edge for a Directed Acyclic Graph

A directed acyclic graph (DAG) is a common topology in biological, engineering, and social networks. A network topology is critical in determining a collective behavior of a network dynamic system. For example, the convergence rate of a consensus behavior in a multiagent system relies on the eigenva...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 67; no. 9; pp. 4885 - 4891
Main Authors Zhang, Hai-Tao, Cao, Haosen, Chen, Zhiyong
Format Journal Article
LanguageEnglish
Published New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Agents and autonomous systems
Biology
Convergence
cooperative control
directed acyclic graphs (DAGs)
Dynamical systems
Eigenvalues
Eigenvalues and eigenfunctions
Laplace equations
Multiagent systems
network analysis and control
Network topologies
Network topology
Social networks
Synchronization
Topology
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Summary:A directed acyclic graph (DAG) is a common topology in biological, engineering, and social networks. A network topology is critical in determining a collective behavior of a network dynamic system. For example, the convergence rate of a consensus behavior in a multiagent system relies on the eigenvalues of the Laplacian associated with the network topology. This article aims to analyze the influence of adding a reverse edge into a DAG on convergence rate. It reveals the existence of the so-called interfering reverse edges; adding one single edge in this category can reduce the so-called dominant convergence rate even for a large network. More specifically, a necessary and sufficient condition of an interfering reverse edge is explicitly constructed. According to the condition, a computationally efficient method is proposed to assess an interfering reverse edge.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2022.3162548