The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate

This paper undertakes an in-depth study and detailed analysis of the problem of the optimal selection of k leaders for a first-order leader-follower multi-agent system (MAS) whose interaction topology is an undirected graph, with the aim of achieving the maximum consensus convergence rate. The conse...

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Main Authors: Shanshan Gao, Chao Ping, Xinzhuang Chen
Format: Article
Language:English
Published: IEEE 2024-01-01
Series:IEEE Access
Subjects:
Online Access:https://ieeexplore.ieee.org/document/10750199/
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author Shanshan Gao
Chao Ping
Xinzhuang Chen
author_facet Shanshan Gao
Chao Ping
Xinzhuang Chen
author_sort Shanshan Gao
collection DOAJ
description This paper undertakes an in-depth study and detailed analysis of the problem of the optimal selection of k leaders for a first-order leader-follower multi-agent system (MAS) whose interaction topology is an undirected graph, with the aim of achieving the maximum consensus convergence rate. The consensus performance of the MAS, which is characterized by the convergence rate, is associated with the algebraic connectivity, which is the smallest nonzero eigenvalue of the interaction topology. Firstly, with the increase in the distance between the followers and the leaders, the entries corresponding to the Fielder vector (the Laplacian eigenvector determined by the algebraic connectivity) also increases. Subsequently, the upper and lower bounds of the algebraic connectivity are obtained with the leader-induced diameter (LID) and the order of the graph. For an interaction topology of leader-follower MAS, it is shown through experiments on generated graphs that the algebraic connectivity has a negative correlation with the LID. Thus, the optimal k-leader selection problem can be approximately transformed into a metric k-center problem, i.e., select k-leader in an undirected graph so that the LID is minimum. Finally, the accuracy of the results was validated through experiments conducted on real networks.
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spelling doaj-art-2150e385b2bc4a17b4e37fdad6cd66822024-11-29T00:01:49ZengIEEEIEEE Access2169-35362024-01-011217564017564610.1109/ACCESS.2024.349583810750199The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence RateShanshan Gao0https://orcid.org/0000-0002-1934-8571Chao Ping1Xinzhuang Chen2https://orcid.org/0000-0002-1782-3535School of Economics and Management, Shanghai University of Electric Power, Shanghai, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi&#x2019;an, Shaanxi, ChinaCollege of Mathematics and Computer Science, Yan&#x2019;an University, Yan&#x2019;an, Shaanxi, ChinaThis paper undertakes an in-depth study and detailed analysis of the problem of the optimal selection of k leaders for a first-order leader-follower multi-agent system (MAS) whose interaction topology is an undirected graph, with the aim of achieving the maximum consensus convergence rate. The consensus performance of the MAS, which is characterized by the convergence rate, is associated with the algebraic connectivity, which is the smallest nonzero eigenvalue of the interaction topology. Firstly, with the increase in the distance between the followers and the leaders, the entries corresponding to the Fielder vector (the Laplacian eigenvector determined by the algebraic connectivity) also increases. Subsequently, the upper and lower bounds of the algebraic connectivity are obtained with the leader-induced diameter (LID) and the order of the graph. For an interaction topology of leader-follower MAS, it is shown through experiments on generated graphs that the algebraic connectivity has a negative correlation with the LID. Thus, the optimal k-leader selection problem can be approximately transformed into a metric k-center problem, i.e., select k-leader in an undirected graph so that the LID is minimum. Finally, the accuracy of the results was validated through experiments conducted on real networks.https://ieeexplore.ieee.org/document/10750199/Leader-follower multi-agent systemsleader-induced diameteralgebraic connectivityconsensus convergence ratemetric k-center problem
spellingShingle Shanshan Gao
Chao Ping
Xinzhuang Chen
The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
IEEE Access
Leader-follower multi-agent systems
leader-induced diameter
algebraic connectivity
consensus convergence rate
metric k-center problem
title The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
title_full The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
title_fullStr The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
title_full_unstemmed The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
title_short The Approach of <italic>k</italic>-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate
title_sort approach of italic k italic leader selection in undirected graphs on maximizing the consensus convergence rate
topic Leader-follower multi-agent systems
leader-induced diameter
algebraic connectivity
consensus convergence rate
metric k-center problem
url https://ieeexplore.ieee.org/document/10750199/
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