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The consensus performance of leader-follower multi-agent systems under reversing the directions of arcs

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  • Song, Xiaodi
  • Zhang, Shenggui
  • Li, Jing
  • Gao, Shanshan

Abstract

A leader-follower multi-agent system (MAS) on a digraph can reach a consensus provided that there exists a directed spanning tree in the digraph. The consensus performance of the MAS, which is characterized by the convergence rate, is associated with the Laplacian spectrum of the digraph. Moreover, the convergence rate increases with an increase on the algebraic connectivity, which is the minimal value among all real parts of nonzero Laplacian eigenvalues of the digraph. To explore the effects of graph operations on convergence rate, we consider the impacts on algebraic connectivity under reversing the directions of arcs among the network between followers in this paper. Consider reversing the direction of one arc, a necessary and sufficient condition for the increase on the algebraic connectivity is proposed based on the entries of a Fiedler vector. What's more, we give some sufficient conditions for the increase or the decrease on the algebraic connectivity under reversing the directions of multiple arcs, respectively.

Suggested Citation

  • Song, Xiaodi & Zhang, Shenggui & Li, Jing & Gao, Shanshan, 2026. "The consensus performance of leader-follower multi-agent systems under reversing the directions of arcs," Applied Mathematics and Computation, Elsevier, vol. 509(C).
    • Handle: RePEc:eee:apmaco:v:509:y:2026:i:c:s0096300325003753
    DOI: 10.1016/j.amc.2025.129649
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    References listed on IDEAS

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    1. Zhao, Can & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo & Liao, Daixi & Zhong, Qishui, 2021. "Leader-following consensus of multi-agent systems via novel sampled-data event-triggered control," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Chen, Liping & Li, Xiaomin & Chen, YangQuan & Wu, Ranchao & Lopes, António M. & Ge, Suoliang, 2022. "Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 414(C).
    3. Sakurama, Kazunori & Miura, Masashi, 2017. "Distributed constraint optimization on networked multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 272-281.
    4. Gao, Shanshan & Zhang, Shenggui & Chen, Xinzhuang & Song, Xiaodi, 2023. "Effects of adding arcs on the consensus convergence rate of leader-follower multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    5. Yang Liu & Dongmei Xie & Lin Shi & Lingling Yao, 2022. "The effect of reverse edges on convergence rate of directed weighted chain network," International Journal of Systems Science, Taylor & Francis Journals, vol. 53(16), pages 3465-3480, December.
    6. Gao, Shanshan & Zhang, Shenggui & Chen, Xinzhuang, 2023. "Effects of changing the weights of arcs on the consensus convergence rate of a leader–follower multi-agent system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Yoo, Sung Jin & Park, Bong Seok, 2022. "A universal error transformation strategy for distributed event-triggered formation tracking of pure-feedback nonlinear multiagent systems with communication and avoidance ranges," Applied Mathematics and Computation, Elsevier, vol. 433(C).
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