Effective augmentation of networked systems and enhancing pinning controllability

Controlling dynamics of networked systems to a reference state, known as pinning control, has many applications in science and engineering. In this paper, we introduce a method for effective augmentation of networked systems, while also providing high levels of pinning controllability for the final augmented network. The problem is how to connect a sub-network to an already existing network such that the pinning controllability is maximised. We consider the eigenratio of the augmented Laplacian matrix as a pinning controllability metric, and use graph perturbation theory to approximate the influence of edge addition on the eigenratio. The proposed metric can be effectively used to find the inter-network links connecting the disjoint networks. Also, an efficient link rewiring approach is proposed to further optimise the pinning controllability of the augmented network. We provide numerical simulations on synthetic networks and show that the proposed method is more effective than heuristic ones.