Inferring Topology of Networked Dynamical Systems by Active Excitations (2208.11276v1)

Abstract: Topology inference for networked dynamical systems (NDSs) has received considerable attention in recent years. The majority of pioneering works have dealt with inferring the topology from abundant observations of NDSs, so as to approximate the real one asymptotically. Leveraging the characteristic that NDSs will react to various disturbances and the disturbance's influence will consistently spread, this paper focuses on inferring the topology by a few active excitations. The key challenge is to distinguish different influences of system noises and excitations from the exhibited state deviations, where the influences will decay with time and the exciatation cannot be arbitrarily large. To practice, we propose a one-shot excitation based inference method to infer $h$-hop neighbors of a node. The excitation conditions for accurate one-hop neighbor inference are first derived with probability guarantees. Then, we extend the results to $h$-hop neighbor inference and multiple excitations cases, providing the explicit relationships between the inference accuracy and excitation magnitude. Specifically, the excitation based inference method is not only suitable for scenarios where abundant observations are unavailable, but also can be leveraged as auxiliary means to improve the accuracy of existing methods. Simulations are conducted to verify the analytical results.