Structural Controllability for a Class of Complex Networks With Root Strongly Connected Components

Structural controllability of complex networks has been an attractive research area, and Minimum Inputs Theorem was proposed to identify the minimum driver nodes for complex networks with one-dimensional node dynamics. Then, the Minimum Inputs Theorem was extended to the complex network with multidimensional node dynamics by looking the multidimensional node as a subnetwork. However, when the structures of these subnetworks possess the root Strongly Connected Components that have perfect matching, the minimum driver nodes of these subnetworks are not sufficient to guarantee the full control, and some extra nodes are needed to be controlled. Therefore, in this paper, we study the structural controllability of complex networks with multidimensional node dynamics whose corresponding subnetworks possess such root Strongly Connected Components. First, we apply the Maximum Matching principle to the network topology to obtain which subnetworks we need to control. Then, an algorithm is proposed to identify a feasible minimum controlled node set of the subnetwork. Finally, by analyzing the structural features of the whole network and synthetically applying the proposed algorithm, Maximum Matching principle and Graphical Approach, a flowchart is given for identifying the minimum controlled node set of the whole network. By duality, the above results can also apply to the structural observability problem of such complex networks.