Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs

TL;DR

This paper introduces a novel algorithm for topology learning in networked linear dynamical systems excited by cyclostationary inputs, extending prior work to complex dependencies and correlated processes, with theoretical guarantees and real-world validation.

Contribution

The paper presents a new algorithm for topology learning in systems with cyclostationary inputs, including complex dependencies, and provides conditions for consistent learning with partial observations.

Findings

Algorithm successfully recovers network topology from cyclostationary inputs.

Theoretical conditions ensure consistent topology learning in bidirected tree networks.

Validated results on simulated and climate data demonstrate effectiveness.

Abstract

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.