Exact controllability of complex networks

Zhengzhong Yuan, Chen Zhao, Zengru Di, Wen-Xu Wang () and Ying-Cheng Lai
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Zhengzhong Yuan: School of Systems Science, Beijing Normal University
Chen Zhao: School of Systems Science, Beijing Normal University
Zengru Di: School of Systems Science, Beijing Normal University
Wen-Xu Wang: School of Systems Science, Beijing Normal University
Ying-Cheng Lai: School of Electrical, Computer and Energy Engineering, Arizona State University

Nature Communications, 2013, vol. 4, issue 1, 1-9

Abstract: Abstract Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.

Date: 2013
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DOI: 10.1038/ncomms3447

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