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

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Hauptverfasser: Doddi, Harish, Deka, Deepjyoti, Salapaka, Murti
Format: Preprint
Veröffentlicht: 2020
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author Doddi, Harish
Deka, Deepjyoti
Salapaka, Murti
author_facet Doddi, Harish
Deka, Deepjyoti
Salapaka, Murti
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2009_12667
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs
Doddi, Harish
Deka, Deepjyoti
Salapaka, Murti
Optimization and Control
Machine Learning
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.
title Topology Learning of unknown Networked Linear Dynamical System excited by Cyclostationary inputs
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2009.12667