Inferring Network Connectivity by Delayed Feedback Control

We suggest a control based approach to topology estimation of networks with N elements. This method first drives the network to steady states by a delayed feedback control; then performs structural perturbations for shifting the steady states M times; and finally infers the connection topology from the steady states' shifts by matrix inverse algorithm (M = N) or l(1)-norm convex optimization strategy applicable to estimate the topology of sparse networks from M << N perturbations. We discuss as well some aspects important for applications, such as the topology reconstruction quality and error sources, advantages and disadvantages of the suggested method, and the influence of (control) perturbations, inhomegenity, sparsity, coupling functions, and measurement noise. Some examples of networks with Chua's oscillators are presented to illustrate the reliability of the suggested technique.