Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme

Lan Wang,Yu Cheng,Jinglu Hu,Jinling Liang,Abdullah M Dobaie

doi:10.1155/2017/8197602

Abstract

Quasi-linear autoregressive with exogenous inputs (Quasi-ARX) models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN) model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.

Highlights

Many real-world systems exhibit complex nonlinear characteristics and cannot be identified directly by linear methods
By using Taylor expansion or other mathematical transformation techniques, a class of ARX-like interfaces is constructed as macro-parts, in which useful properties of linear models can be introduced, while their coefficients are represented by some nonlinear models such as radial basis function networks (RBFNs)
From the simulation results under a short training sequence (100 samples), it is seen that when the design parameters are optimized, support vector regression (SVR) with quasi-linear kernel performs much better than the ones with Gaussian kernel and linear kernel, and the quasi-linear kernel performs little sensitively with respect to the SVR super-parameter setting

Summary

Introduction

Many real-world systems exhibit complex nonlinear characteristics and cannot be identified directly by linear methods. The macro-part is a user-friendly interface favorable to specific applications, and the core-part is used to represent the complicated coefficients of the macro-part To this end, by using Taylor expansion or other mathematical transformation techniques, a class of ARX-like interfaces is constructed as macro-parts, in which useful properties of linear models can be introduced, while their coefficients are represented by some nonlinear models such as RBFNs. To this end, by using Taylor expansion or other mathematical transformation techniques, a class of ARX-like interfaces is constructed as macro-parts, in which useful properties of linear models can be introduced, while their coefficients are represented by some nonlinear models such as RBFNs In this way, a quasiARX predictor linear with input variable u(t) can be further designed, where u(t) in the core-part is replaced skillfully by an extra variable.

Objectives

Methods

Conclusion