Identification and control of nonlinear systems using PieceWise Auto-Regressive eXogenous models

Abstract

In this paper, we consider the problems of nonlinear system representation and control. In fact, we propose a solution based on PieceWise Auto-Regressive eXogenous (PWARX) models since these models are able to approximate any nonlinear behaviour with arbitrary precision. Moreover, the identification and control approaches of linear systems can be extended to these models because the parameters of each sub-model are linearly related to the output. The proposed solution is based on two steps. The first allows to represent the nonlinear system by a PWARX model using the identification approach. The second consists in designing a controller for each sub-model using the pole placement strategy. Simulation and experimental results are presented to illustrate the performance of the proposed approach.

Extension of a clustering identification approach to multivariable piecewise affine systems: Application to an industrial dryer

“…After that, similar and close ARX models are then grouped in clusters using a convenient clustering technique. 33,34 Finally, clusters in the regressor space are separated by hyperplanes using linear classification technique such as the SVM appraoch. 35 Obviously, data classification is the cornerstone for successful identification of PWA systems.…”

“…36 The proposed identification approach is based on the DBSCAN (Density Based Spatial Clustering of Applications with Noise) clustering technique which has proven its performance with the SISO (Single Input Single Output) PWA systems. 34 However, for MIMO PWA systems the dimension of the matrices of parameters to be classified affects the concept of research of similar objects which is based on the measure of distances. Added to that, the choice of the synthesis parameters of this method becomes more difficult because identifying the same number of objects in a given neighborhood needs a large radius which will influence the resulting clusters.…”

Extension of the clustering identification by extending the Density Based Spatial Clustering of Applications with Noise approach to Multi-Input Multi-Output Piece Wise Affine systems: Application to an industrial robot

“…For each one, an ARX model is identified using least squares. After that, similar ARX models are assembled into clusters by the use of a convenient clustering technique Lassoued and Abderrahim (2019), Lassoued and Abderrahim (2014a). Finally, the obtained clusters are delimited with hyperplanes using the Supprot Vector Machine (SVM) approach Wang (2005).…”

Determinação da Estrutura de Modelos PWARX com Base no Erro Dinâmico de Predição

“…Nosúltimos anos, tem-se observado um empenho crescente em técnicas de identificação de sistemas com modelos afim chaveados (do inglês -switched affine models) (Du et al, 2018;Zwart, 2019;Hojjatinia et al, 2019;Fey et al, 2020) e modelos afim por partes (do inglês -piecewise affine models) (Barbosa et al, 2018;Schirrer et al, 2018;Lassoued e Abderrahim, 2019;Kersting e Buss, 2019;Du et al, 2020). Isto se deve ao fato de que identificar um modelo global que consiga cobrir diversas situações pode torná-lo muito complexo.…”

“…Trabalhos presentes na literatura com a identificação dessa classe de modelo ainda carecem de atenção quantoà escolha dos regressores que irão compor o vetor de regressores, como exemplos, (Nakada et al, 2005;Sun et al, 2018;Lassoued e Abderrahim, 2019;Du et al, 2020). O presente trabalho tem como foco a escolha de diferentes regressores nesse tipo de representação.…”