DATA FILTERING BASED STOCHASTIC GRADIENT ALGORITHMS FOR MULTIVARIABLE CARAR-LIKE SYSTEMS

Dongqing Wang,Rui Ding,Tong Shan

doi:10.3846/13926292.2013.804889

Abstract

This paper considers identification problems for a multivariable controlled autoregressive system with autoregressive noises. A hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm are presented to estimate the parameter vectors and parameter matrix of such multivariable colored noise systems, by using the hierarchical identification principle. The simulation results show that the proposed hierarchical gradient estimation algorithms are effective.

Highlights

Multivariable system modelling has received much attention in various practical systems, including magnetic compressors and magnetic fluids [9, 17], piston engines [8], distillation columns [13, 14], fault detection systems [12, 18] and travelling waves [11], etc
As a consequence of this wide variety of applications, different identification algorithms for multivariable systems have been vastly reported in the literature, e.g., the gradient based iterative algorithm and the least squares based iterative algorithm for multivariable CARARMA systems [7], the hierarchical gradient-based iterative identification algorithms for multivariable CARAR-like systems [21], the stochastic gradient estimation algorithm for multivariable equation error systems [15], the auxiliary modelbased multi-innovation stochastic gradient algorithm for multiple-input singleoutput systems [16], the bias compensation based identification algorithms for multivariable systems [22, 23], and the coupled-least-squares identification for multivariable systems [1]
On the basis of the above research, this paper studies the identification problems for multivariable controlled autoregressive systems with autoregressive colored noises by using the data filtering technique [19,20] and the hierarchical identification principle [4,5]

Summary

Introduction

Multivariable system modelling has received much attention in various practical systems, including magnetic compressors and magnetic fluids [9, 17], piston engines [8], distillation columns [13, 14], fault detection systems [12, 18] and. A filtering based hierarchical stochastic gradient (F-HSG) algorithm is presented to estimate the parameters of the multivariable CARAR-like system by combining the filtering technique [19, 20] and the hierarchical identification principle [4, 5]. The basic idea of the F-HSG algorithm is to use a rational polynomial to filter the input-output data of the system, to transform a multivariable CARAR-like system into two identification models: a multivariable ARX-like system model which is parametrised by a parameter matrix and a parameter vector, and a multivariable AR noise model which is parametrised by only a parameter vector, and to estimate the system parameter matrix and the two parameter vectors in an alternating manner by using the hierarchical identification principle.

Hierarchical Generalized Stochastic Gradient Algorithm

Filtering Based Hierarchical Stochastic Gradient Algorithm

Example

Conclusions