Data-based system representations from irregularly measured data

TL;DR

This paper introduces a kernel-based approach to derive system representations from irregularly sampled data, enabling data completion and analysis even with missing or noisy measurements.

Contribution

It develops computational methods leveraging kernel structures of Hankel matrices for system representation from incomplete data, including conditions for periodic missing data.

Findings

Method effectively reconstructs system behavior from irregular data.

Applicable to real-world data completion tasks.

Performs well compared to alternative methods.

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.