Title: An introduction to models based on Laguerre, Kautz and other related orthonormal functions – part I: linear and uncertain models

Authors: Gustavo H.C. Oliveira, Alex Da Rosa, Ricardo J.G.B. Campello, Jeremias B. Machado, Wagner C. Amaral

Addresses: Department of Electrical Engineering, Federal University of Parana (UFPR), 80215-901, Curitiba-PR, Brazil. ' Department of Electrical Engineering, University of Brasilia (UnB), 70910-900, Brasilia-DF, Brazil. ' Department of Computer Sciences, University of Sao Paulo (USP), 13560-970, Sao Carlos-SP, Brazil. ' Engineering and Information Technology Institute, Federal University of Itajuba (UNIFEI), 37500-903, Itajuba-MG, Brazil. ' School of Electrical and Computer Engineering, University of Campinas (UNICAMP), 13083-852, Campinas-SP, Brazil

Abstract: This paper provides an overview of system identification using orthonormal basis function models, such as those based on Laguerre, Kautz, and generalised orthonormal basis functions. The paper is separated in two parts. In this first part, the mathematical foundations of these models as well as their advantages and limitations are discussed within the context of linear and robust system identification. The second part approaches the issues related with non-linear models. The discussions comprise a broad bibliographical survey of the subjects involving linear models within the orthonormal basis functions framework. Theoretical and practical issues regarding the identification of these models are presented and illustrated by means of a case study involving a polymerisation process.

Keywords: modelling; linear system identification; robust identification; orthonormal basis functions; OBF; linear systems; uncertainty; polymerisation.

DOI: 10.1504/IJMIC.2011.042346

International Journal of Modelling, Identification and Control, 2011 Vol.14 No.1/2, pp.121 - 132

Published online: 21 Mar 2015 *

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