Exploring the links between the fundamental lemma and kernel regression

Publikationstyp
Journal Article
Date Issued
2024-05-27
Sprache
English
Author(s)
Molodchyk, Oleksii  
Regelungstechnik E-14  
Faulwasser, Timm  
Regelungstechnik E-14  
TORE-URI
https://hdl.handle.net/11420/48813
Journal
IEEE control systems letters  
Volume
8
Start Page
2045
End Page
2050
Citation
IEEE Control Systems Letters 8: 2045 - 2050 (2024-05-27)
Publisher DOI
10.1109/LCSYS.2024.3406053
Scopus ID
2-s2.0-85194831807
Publisher
Institute of Electrical and Electronics Engineers Inc.
Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.
Subjects
data-driven control
kernel regression
reproducing kernel Hilbert space
System identification
DDC Class
005: Computer Programming, Programs, Data and Security
519: Applied Mathematics, Probabilities