MINIMAL EDGE CONTROLLABILITY OF DIRECTED NETWORKS

Linying Xiang () and Guanrong Chen
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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

Advances in Complex Systems (ACS), 2019, vol. 22, issue 07n08, 1-23

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.

Keywords: Minimal controllability; cycle; edge dynamics; directed network; signed graph (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219525919500176

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