Parameter Set-mapping using Kernel-based PCA for Linear Parameter Varying Systems

S. Z. Rizvi, J. Mohammadpour, R. Toth, N. Meskin

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

7 Citations (Scopus)

Abstract

This paper proposes a method for reduction of scheduling dependency in linear parameter-varying (LPV) systems. In particular, both the dimension of the scheduling variable and the corresponding scheduling region are shrunk using kernel-based principal component analysis (PCA). Kernel PCA corresponds to linear PCA that is performed in a high-dimensional feature space, allowing the extension of linear PCA to nonlinear dimensionality reduction. Hence, it enables the reduction of complicated coefficient dependencies which cannot be simplified in a linear subspace, giving kernel PCA an advantage over other linear techniques. This corresponds to mapping the original scheduling variables to a set of lower dimensional variables via a nonlinear mapping. However, to recover the original coefficient functions of the model, this nonlinear mapping is needed to be inverted. Such an inversion is not straightforward. The reduced scheduling variables are a nonlinear expansion of the original scheduling variables into a high-dimensional feature space, an inverse mapping for which is not available. Therefore, we cannot generally assert that such an expansion has a "pre-image" in the original scheduling region. While certain pre-image approximation algorithms are found in the literature for Gaussian kernel-based PCA, we aim to generalize the pre-image estimation algorithm to other commonly used kernels, and formulate an iterative pre-image estimation rule. Finally, we consider the case study of a physical system described by an LPV model and compare the performance of linear and kernel PCA-based LPV model reduction.
Original languageEnglish
Title of host publicationProceedings of the 13th European Control Conference (ECC), 24-27 July 2014, Strasbourg, France
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages2744-2749
ISBN (Print)978-3-9524269-1-3
DOIs
Publication statusPublished - 2014
Event13th European Control Conference, (ECC 2014) - University of Strasbourg, Strasbourg, France
Duration: 24 Jun 201427 Jun 2014
Conference number: 13
https://www.ieee.org/conferences_events/conferences/conferencedetails/index.html?Conf_ID=33336

Conference

Conference13th European Control Conference, (ECC 2014)
Abbreviated titleECC 2014
CountryFrance
CityStrasbourg
Period24/06/1427/06/14
Other2014 European Control Conference
Internet address

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