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Volume 6 Issue 5
Sep.  2019

IEEE/CAA Journal of Automatica Sinica

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Xichen Wang, Yugeng Xi, Wenzhen Huang and Shuai Jia, "Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network's Structural Controllability," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1152-1165, Sept. 2019. doi: 10.1109/JAS.2017.7510724
Citation: Xichen Wang, Yugeng Xi, Wenzhen Huang and Shuai Jia, "Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network's Structural Controllability," IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1152-1165, Sept. 2019. doi: 10.1109/JAS.2017.7510724

Deducing Complete Selection Rule Set for Driver Nodes to Guarantee Network's Structural Controllability

doi: 10.1109/JAS.2017.7510724
Funds:

the National Science Foundation of China 61333009

the National Science Foundation of China 61473317

the National Science Foundation of China 61433002

the National Science Foundation of China 61521063

the National Science Foundation of China 61590924

the National Science Foundation of China 61673366

the National High Technology Research and Development Program of China 2015AA043102

More Information
  • Structural controllability is critical for operating and controlling large-scale complex networks. In real applications, for a given network, it is always desirable to have more selections for driver nodes which make the network structurally controllable. Different from the works in complex network field where structural controllability is often used to explore the emergence properties of complex networks at a macro level, in this paper, we investigate it for control design purpose at the application level and focus on describing and obtaining the solution space for all selections of driver nodes to guarantee structural controllability. In accord with practical applications, we define the complete selection rule set as the solution space which is composed of a series of selection rules expressed by intuitive algebraic forms. It explicitly indicates which nodes must be controlled and how many nodes need to be controlled in a node set and thus is particularly helpful for freely selecting driver nodes. Based on two algebraic criteria of structural controllability, we separately develop an input-connectivity algorithm and a relevancy algorithm to deduce selection rules for driver nodes. In order to reduce the computational complexity, we propose a pretreatment algorithm to reduce the scale of network's structural matrix efficiently, and a rearrangement algorithm to partition the matrix into several smaller ones. A general procedure is proposed to get the complete selection rule set for driver nodes which guarantee network's structural controllability. Simulation tests with efficiency analysis of the proposed algorithms are given and the result of applying the proposed procedure to some real networks is also shown, and these all indicate the validity of the proposed procedure.

     

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    Highlights

    • Control design needs more selections of driver nodes with structural controllability.
    • Complete selection rule set gives an intuitive solution space and is easy to use.
    • A general procedure to deduce the complete selection rule set is proposed.
    • Four algorithms are developed to improve the computational efficiency.
    • The derived selection rule set is proved complete based on theoretical analysis.

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