Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies
This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/4096981 |
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| _version_ | 1832554684202614784 |
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| author | Yujuan Han Wenlian Lu Tianping Chen Changkai Sun |
| author_facet | Yujuan Han Wenlian Lu Tianping Chen Changkai Sun |
| author_sort | Yujuan Han |
| collection | DOAJ |
| description | This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results. |
| format | Article |
| id | doaj-art-f7d04bebbc594d8090e4e6997ddf1b2d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-f7d04bebbc594d8090e4e6997ddf1b2d2025-02-03T05:50:51ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/40969814096981Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph TopologiesYujuan Han0Wenlian Lu1Tianping Chen2Changkai Sun3College of Information Engineering, Shanghai Maritime University, Shanghai, ChinaSchool of Mathematical Sciences, Institute of Science and Technology for Brain-Inspired Intelligence, Shanghai Center for Mathematical Sciences, The Laboratory of Mathematics for Nonlinear Science and the Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University, Shanghai, ChinaSchool of Computer Sciences and Mathematical Sciences, Fudan University, Shanghai, ChinaResearch & Educational Center for the Control Engineering of Translational Precision Medicine (R-ECCE-TPM), Dalian University of Technology, Dalian, ChinaThis paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results.http://dx.doi.org/10.1155/2019/4096981 |
| spellingShingle | Yujuan Han Wenlian Lu Tianping Chen Changkai Sun Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies Complexity |
| title | Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies |
| title_full | Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies |
| title_fullStr | Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies |
| title_full_unstemmed | Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies |
| title_short | Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies |
| title_sort | optimizing pinned nodes to maximize the convergence rate of multiagent systems with digraph topologies |
| url | http://dx.doi.org/10.1155/2019/4096981 |
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