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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2024-01-01
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| 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 |
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| 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. |
| format | Article |
| id | doaj-art-2150e385b2bc4a17b4e37fdad6cd6682 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
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| series | IEEE Access |
| 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’an, Shaanxi, ChinaCollege of Mathematics and Computer Science, Yan’an University, Yan’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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