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Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies

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  • Yujuan Han
  • Wenlian Lu
  • Tianping Chen
  • Changkai Sun

Abstract

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.

Suggested Citation

  • Yujuan Han & Wenlian Lu & Tianping Chen & Changkai Sun, 2019. "Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    • Handle: RePEc:hin:complx:4096981
    DOI: 10.1155/2019/4096981
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    References listed on IDEAS

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    1. Wang, Xiao Fan & Chen, Guanrong, 2002. "Pinning control of scale-free dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 521-531.
    2. Zou, Yanli & Chen, Guanrong, 2009. "Choosing effective controlled nodes for scale-free network synchronization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2931-2940.
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