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Minimal Edge Controllability Of Directed Networks

Author

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  • LINYING XIANG

    (School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, Hebei 066004, P. R. China)

  • GUANRONG CHEN

    (Department of Electrical Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China)

Abstract

Minimal edge controllability of directed networks is investigated in this paper. A new edge dynamics model is first introduced with two nonzero parameters describing the linear relationship between the node states and the edge states. Three different digraphs as skeleton structures for minimal edge controllability are analyzed. The conditions ensuring both node controllability and edge controllability for these three digraphs are presented, respectively. It is found that cycles in these networks play an important role in edge controllability. The notion of minimal edge controllability is then extended to signed digraphs. It is shown that the minimal edge controllability of a signed cycle depends on the number of edges with negative weights, regardless of the placement of the negative weights on the edges. Some examples are presented for illustration and verification.

Suggested Citation

  • Linying Xiang & Guanrong Chen, 2019. "Minimal Edge Controllability Of Directed Networks," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-23, December.
    • Handle: RePEc:wsi:acsxxx:v:22:y:2019:i:07n08:n:s0219525919500176
    DOI: 10.1142/S0219525919500176
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    References listed on IDEAS

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    1. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
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    Cited by:

    1. Aming Li & Yang-Yu Liu, 2020. "Controlling Network Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 22(07n08), pages 1-19, February.

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