Identifiability and Identification of Switching Dynamical Networks: A Data-Based Approach

In this article, we investigate the identifiability and identification problem of switching (directed) dynamical networks (SDNs) modeled by switched linear dynamical systems. Switching signals governing the active subsystem (mode) are frequently changing, which brings challenges to the exact reconstruction of network sequences, since the state trajectory is generated by a number of subsystems at different time periods. By analyzing unobservable subspaces associated with each subsystem, we first establish necessary and/or sufficient conditions for the identifiability of SDNs under different levels of knowledge on the switching signal. Building on this, a sufficient identification condition is developed leveraging coupled Lyapunov-transpose matrix equations constructed by state trajectories with properly designed time offsets, which allows us to design a data-based approach that can exactly recover the whole network sequence, even if the switching signal is unknown a priori. More important, we develop sharper conditions for both identifiability and identification when there is certain prior knowledge available on networks. Numerical experiments on switching consensus networks and sparse networks are conducted to verify the effectiveness of the theoretical findings.