Title: Kernel-enabled methods for subspace regression and efficient control

Authors: Kaustubh Patil, Abhijit Kulkarni

Addresses: LIADD/INESC Porto LA, University of Porto, Porto, Portugal. ' Tata Research Development and Design Centre (TRDDC), 54B, Hadapsar Industrial Estate, Pune 411 013, India

Abstract: Due to many inherent desirable properties, kernel-based formalisms are quite popular and find many applications in diverse areas. They are routinely applied to solve important class of three machine learning problems viz. pattern classification, function approximation and density estimation. In the present work, three kernel variants of traditional algorithms viz. Principal Component Regression (PCR), Partial Least Squares (PLS) regression and Recursive Least Squares (RLS)regression are used and compared on two benchmark problems viz. Henon map and problem due to Narendra and Li. All the methods performed equally well. These methods are found to be robust in presence of noise also. Owing to its adaptive nature, Kernel Recursive Least Squares (KRLS) was used in controlling the above non-linear systems with set point stabilisation and trajectory tracking as two control objectives. KRLS performed well on all the systems for both the control objectives. In general, it was found that kernel-based formalisms deal effectively with the non-linearity in the data thereby making subspace regression and control accurate.

Keywords: kernel RLS; PCR; principal component regression; PLS; partial least squares; recursive least squares; subspace regression; nonlinear control; set point stabilisation; trajectory tracking.

DOI: 10.1504/IJMIC.2008.022019

International Journal of Modelling, Identification and Control, 2008 Vol.5 No.2, pp.136 - 145

Published online: 16 Dec 2008 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article