A comparison of manifold regularization approaches for kernel-based system identification

M. Mazzoleni, M. Scandella, F. Previdi

Abstract

In this paper, we present a simulation study to investigate the role of manifold regularization in kernel-based approaches for nonparametric nonlinear SISO (Single-Input Single-Output) system identification. This problem is tackled as the estimation of a static nonlinear function that maps regressors (that contain past values of both input and output of the dynamic system) to the system outputs. Manifold regularization, as opposite to the Tikhonov one, enforces a local smoothing constraint on the estimated function. It is based on the assumption that the regressors lie on a manifold in the regressors space. This manifold is usually approximated with a weighted graph that connects the regressors. The present work analyzes the performance of kernel-based methods estimates when different choices are made for the graph connections and their respective weights. The approach is tested on benchmark nonlinear systems models, for different connections and weights strategies. Results give an intuition about the most promising choices in order to adopt manifold regularization for system identification [Paper, Code]

Reference

M. Mazzoleni, M. Scandella, F. Previdi, "A comparison of manifold regularization approaches for kernel-based system identification", IFAC Adaptive and Learning Control Systems (ALCOS) conference, 2019. , doi: 10.1016/j.ifacol.2019.12.641 ISSN: 2405-8963, IFAC-PapersOnLine, vol. 52, issue 29, pp. 180-185.

Bibtex

@article{MAZZOLENI2019180,
title = "A comparison of manifold regularization approaches for kernel-based system identification",
journal = "IFAC-PapersOnLine",
volume = "52",
number = "29",
pages = "180 - 185",
year = "2019",
note = "13th IFAC Workshop on Adaptive and Learning Control Systems ALCOS 2019",
issn = "2405-8963",
doi = "https://doi.org/10.1016/j.ifacol.2019.12.641",
url = "http://www.sciencedirect.com/science/article/pii/S2405896319325868",
author = "M. Mazzoleni and M. Scandella and F. Previdi",
}