A Loewner Matrix Based Convex Optimization Approach to Finding Low Rank Mixed Time/Frequency Domain Interpolants

We consider the problem of finding the lowest order stable rational transfer function that interpolates a set of given noisy time and frequency domain data points. Our main result shows that exploiting results from rational interpolation theory allows for recasting this problem as minimizing the ran...

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Bibliographic Details
Published inProceedings of the American Control Conference pp. 5169 - 5174
Main Authors Singh, Rajiv, Sznaier, Mario
Format Conference Proceeding
LanguageEnglish
Published AACC 01.07.2020
Subjects
Data models
Interpolation
Noise measurement
Time-domain analysis
Time-frequency analysis
Transfer functions
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Summary:We consider the problem of finding the lowest order stable rational transfer function that interpolates a set of given noisy time and frequency domain data points. Our main result shows that exploiting results from rational interpolation theory allows for recasting this problem as minimizing the rank of a matrix constructed from the frequency domain data (the Loewner matrix) along with the Hankel matrix of time domain data, subject to a semidefinite constraint that enforces stability and consistency between the time and frequency domain data. These results are applied to a practical problem: identifying a system from noisy measurements of its time and frequency responses. The proposed method is able to obtain stable low order models using substantially smaller matrices than those reported earlier and consequently in a fraction of the computation time.
ISSN:2378-5861
DOI:10.23919/ACC45564.2020.9147366