Pinning control and controllability of complex dynamical networks
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In this article, the notion of pinning control for directed networks of dynamical systems is introduced, where the nodes could be either single-input single-output (SISO) or multi-input multi-output (MIMO) dynamical systems, and could be non-identical and nonlinear in general but will be specified to be identical linear time-invariant (LTI) systems here in the study of network controllability. Both state and structural controllability problems will be discussed, illustrating how the network topology, node-system dynamics, external control inputs and inner dynamical interactions altogether affect the controllability of a general complex network of LTI systems, with necessary and sufficient conditions presented for both SISO and MIMO settings. To that end, the controllability of a special temporally switching directed network of linear time-varying (LTV) node systems will be addressed, leaving some more general networks and challenging issues to the end for research outlook.
KeywordsComplex network pinning control controllability linear time-invariant (LTI) system temporally switching network graph theory
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The author thanks Mario di Bernardo, Jian-Xi Gao, Bao- Yu Hou, Xiang Li, Yang-Yu Liu, LinWang, Xiao-FanWang, Lin-Ying Xiang and Gang Yan for their valuable comments and discussions.
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