Data-based System Representations from Irregularly Measured Data

verfasst von: Mohammad Salahaldeen Ahmad Alsalti, Ivan Markovsky, Victor Gabriel Lopez Mejia, Matthias A. Müller
Abstract: Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult task. By exploiting the kernel structure of Hankel matrices of irregularly measured data generated by a linear time-invariant system, we provide computational methods for which any complete finite-length behavior of the system can be obtained. For the special case of periodically missing outputs, we provide conditions on the input such that the former result is guaranteed. In the presence of noise in the data, our method returns an approximate finite-length behavior of the system. We illustrate our result with several examples, including its use for approximate data completion in real-world applications and compare it to alternative methods.
Organisationseinheit(en): Institut für Regelungstechnik
Externe Organisation(en): Institució Catalana de Recerca i Estudis Avançats (ICREA)
International Centre for Numerical Methods in Engineering
Typ: Artikel
Journal: IEEE Transactions on Automatic Control
Band: 70
Seiten: 143 - 158
Anzahl der Seiten: 16
ISSN: 0018-9286
Publikationsdatum: 04.07.2024
Publikationsstatus: Veröffentlicht
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Elektrotechnik und Elektronik, Steuerungs- und Systemtechnik, Angewandte Informatik
Elektronische Version(en): https://doi.org/10.48550/arXiv.2307.11589 (Zugang: Offen)
https://doi.org/10.1109/TAC.2024.3423053 (Zugang: Geschlossen)

BibTeX

@article{5d355750d91d4279b3b204d3b98ab410,
title = "Data-based System Representations from Irregularly Measured Data",
abstract = "Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult task. By exploiting the kernel structure of Hankel matrices of irregularly measured data generated by a linear time-invariant system, we provide computational methods for which any complete finite-length behavior of the system can be obtained. For the special case of periodically missing outputs, we provide conditions on the input such that the former result is guaranteed. In the presence of noise in the data, our method returns an approximate finite-length behavior of the system. We illustrate our result with several examples, including its use for approximate data completion in real-world applications and compare it to alternative methods.",
keywords = "Biomedical measurement, Dynamical systems, Kernel, Linear systems, Noise measurement, Time series analysis, Trajectory, Behavioral system theory, data-based representations, irregular measurements",
author = "Alsalti, {Mohammad Salahaldeen Ahmad} and Ivan Markovsky and {Lopez Mejia}, {Victor Gabriel} and M{\"u}ller, {Matthias A.}",
note = "Publisher Copyright: IEEE",
year = "2024",
month = jul,
day = "4",
doi = "10.48550/arXiv.2307.11589",
language = "English",
volume = "70",
pages = "143 -- 158",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "1",
}