Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs
This work addresses topology learning for networked systems, which is crucial for control and cybersecurity, but is incremental as it extends prior methods to handle cyclostationary inputs and complex dependencies.
The authors tackled the problem of topology learning for networked linear dynamical systems excited by cyclostationary inputs, developing a novel algorithm that guarantees learning and applies to complex-valued dependencies, validated on simulated and real-world climate data with consistent recovery of full topologies including unobserved nodes.
Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on dynamical systems excited by temporally uncorrelated processes. In this article, we present a novel algorithm for guaranteed topology learning of networks that are excited by temporally (colored) cyclostationary processes, which encompasses a wide range of temporal correlation including wide-sense stationarity. Furthermore, unlike prior work, the framework applies to linear dynamic system with complex valued dependencies, and leverages group lasso regularization for effective learning of the network structure. In the second part of the article, we analyze conditions for consistent topology learning for bidirected tree networks when a subset of the network is unobserved. Here, the full topology along with unobserved nodes are recovered from observed node's time-series alone. Our theoretical contributions are validated on simulated data as well as on real-world climate data.