Computing structural controllability of linearly-coupled complex networks

Structural controllability, as a generic structure-based property in determining the ability of a complex network to reach the desired configuration, is addressed in this work. Using a robust measure derived from robust control theory, this paper deals with structural controllability of a type of weighted network of networks (NetoNets) involving linear couplings between its corresponding networks and clusters. Unlike the structural controllability degrees rooted in graph theory, this paper takes the advantage of uncertain systems to define the notion of structural controllability in a straightforward and less computationally complex way. Moreover, the spectrum of required energy is discussed. Eventually, the results for the proposed measure of structural controllability of scale-free networks are given to justify the proposed measure of an efficient and effective guarantee for fully controllability of the NetoNets in exposure to cluster and network-dependency connections. The proposed measure is an optimal solution according to structural energy-related control of the NetoNet where the upper bound of the required energy is illustrated an efficient measure for structural controllability of the class of NetoNet. Arbitrarily connectivity of low connected vertices to their higher connected counterparts in clusters results in effective controllability. In the same direction, as seminal works in structural controllability of complex networks to avoid the highly-connected nodes, the larger the cluster/network connectivity degree is, the less fully controllability of NetoNet is guaranteed.