TY - JOUR

T1 - Data-based System Representations from Irregularly Measured Data

AU - Alsalti, Mohammad Salahaldeen Ahmad

AU - Markovsky, Ivan

AU - Lopez Mejia, Victor Gabriel

AU - Müller, Matthias A.

N1 - Publisher Copyright: IEEE

PY - 2024/7/4

Y1 - 2024/7/4

N2 - 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.

AB - 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.

KW - Biomedical measurement

KW - Dynamical systems

KW - Kernel

KW - Linear systems

KW - Noise measurement

KW - Time series analysis

KW - Trajectory

KW - Behavioral system theory

KW - data-based representations

KW - irregular measurements

UR - http://www.scopus.com/inward/record.url?scp=85197481941&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2307.11589

DO - 10.48550/arXiv.2307.11589

M3 - Article

VL - 70

SP - 143

EP - 158

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 1

ER -