Recursive Identification Methods For Multivariate Equation-Error Systems

Multivariate systems exist widely in the field of practical industrial control.As a kind of identification model of multivariate systems,the multivariate equation-error systems can represent both linear multivariate system and a class of nonlinear multivariate system.Data filtering technology,coupling identification concept and multi-innovation theory are new identification methods in recent years.For multivariate equation-error systems,combing traditional recursive identification methods with new technologies and new concepts,proposing some new identification algorithms,which is of great benefit to improving the estimation accuracy and identification speed.This paper mainly studies the recursive identification methods for multivariate equation-error systems under the interference of colored noise.The major results are as follows.1 For the multivariate equation-error systems with the moving average colored noise,the original system is decomposed into two sub-identification models including the system parameter vector and the noise parameter vector respectively by using the decomposition technology.A decomposition based extended stochastic gradient algorithm is proposed.In order to improve the identification speed and algorithm parameters estimation accuracy,a decomposition based multi-innovation extended stochastic gradient algorithm is deduced by introducing the multi-innovation theory.A decomposition based recursive extended least square algorithm is proposed by combining the least squares principle with the decomposition technique.2 For the multivariate equation-error systems with the autoregressive colored noise,a recursive generalized least square algorithm is given firstly.In order to reduce redundant calculation of parameter estimation,a partially coupled recursive generalized least square algorithm is proposed by using the coupling identification concept which can connect each subsystem parameter estimates.A partially coupled generalized stochastic gradient algorithm is proposed by combining the negative gradient search principle with the coupling identification concept.A partially coupled multiinnovation generalized stochastic gradient algorithm is derived by introducing the multi-innovation theory.3 For the multivariate equation-error systems with the autoregressive moving average colored noise,to reduce the parameter estimation effect of the colored noise in the generalized extended stochastic gradient algorithm,a filtering based multivariate generalized extended stochastic gradient algorithm is proposed by using a filter to filter the input and output data,which can transform the colored noise into white noise.In order to obtain higher parameters estimation accuracy,a filtering based multivariate multi-innovation generalized extended stochastic gradient algorithm is derived by using the multi-innovation theory.A filtering based multivariate recursive generalized extended least square algorithm is proposed by combining the data filtering technique and the least squares principle.The proposed algorithms' operation steps and flow charts are given in this paper.The calculation amount of some algorithms are compared and analyzed.The numerical simulation experiments are carried out and the detailed experimental results are given.They verifies the good parameter estimation performances of the proposed algorithms.