Data-Based System Representations From Irregularly Measured Data

• 成果类型: Article
• 署名作者: Alsalti, Mohammad; Markovsky, Ivan; Lopez, Victor G.; Mueller, Matthias A.
• 署名单位: Leibniz University Hannover; Universitat Politecnica de Catalunya; Centre Internacional de Metodes Numerics en Enginyeria (CIMNE); ICREA
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3423053
• 发表日期: 2025
• 页码: 143-158
• 关键词: Kernel; trajectory; Linear systems; dynamical systems; Noise measurement; Biomedical measurement; time series analysis; Behavioral system theory; data-based representations; irregular measurements

摘要

Nonparametric 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.