Sampling and inference of networked dynamics using Log-Koopman nonlinear graph fourier transform

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dc.contributor.authorWei, Zhuangkun
dc.contributor.authorLi, Bin
dc.contributor.authorSun, Chengyao
dc.contributor.authorGuo, Weisi
dc.date.accessioned2020-12-11T16:52:41Z
dc.date.available2020-12-11T16:52:41Z
dc.date.issued2020-10-21
dc.description.abstractMonitoring the networked dynamics via the subset of nodes is essential for a variety of scientific and operational purposes. When there is a lack of an explicit model and networked signal space, traditional observability analysis and non-convex methods are insufficient. Current data-driven Koopman linearization, although derives a linear evolution model for selected vector-valued observable of original state-space, may result in a large sampling set due to: (i) the large size of polynomial based observables (O(N2) , N number of nodes in network), and (ii) not factoring in the nonlinear dependency betweenobservables. In this work, to achieve linear scaling (O(N) ) and a small set of sampling nodes, wepropose to combine a novel Log-Koopman operator and nonlinear Graph Fourier Transform (NL-GFT) scheme. First, the Log-Koopman operator is able to reduce the size of observables by transforming multiplicative poly-observable to logarithm summation. Second, anonlinear GFT concept and sampling theory are provided to exploit the nonlinear dependence of observables for observability analysis using Koopman evolution model. The results demonstrate that the proposed Log-Koopman NL-GFT scheme can (i) linearize unknownnonlinear dynamics using O(N) observables, and (ii) achieve lower number of sampling nodes, compared with the state-of-the art polynomial Koopman based observability analysis.en_UK
dc.identifier.citationWei Z, Li B, Sun C, Guo W. (2020) Sampling and inference of networked dynamics using Log-Koopman nonlinear graph fourier transform. IEEE Transactions on Signal Processing, Volume 68, October 2020, pp. 6187-6197en_UK
dc.identifier.issn1053-587X
dc.identifier.urihttps://doi.org/10.1109/TSP.2020.3032408
dc.identifier.urihttps://dspace.lib.cranfield.ac.uk/handle/1826/16085
dc.language.isoenen_UK
dc.publisherIEEEen_UK
dc.rightsAttribution-NonCommercial 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/*
dc.subjectNetwork dynamicsen_UK
dc.subjectsensor placementen_UK
dc.subjectKoopman operatoren_UK
dc.subjectGraph Fourier Transformen_UK
dc.subjectcompressionen_UK
dc.titleSampling and inference of networked dynamics using Log-Koopman nonlinear graph fourier transformen_UK
dc.typeArticleen_UK

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