Gradient Identification For Multivariable Equation-Error Systems Based On The Filtering Technique

Multivariable control system has the characteristics of complex structure and many parameters.With the development of modern society,many economic system and social system is multivariate.This paper researches on the problems of parameters identification of multivariable system,which have an important significance to the analysis,synthesis and design of multivariable control system.This paper uses the data filtering technique and gradient search method to study the problems of parameters identification of equation error systems.The research results as follows.(1)For multivariable equation error moving average systems,firstly using the data filtering technology to preprocess input and output data,the system is divided into two subsystems,a system model including system parameters and a noise model including noise parameters.The unpredictable noise of information vector in the identification model is replaced by the last moment estimation and then gradient search method is used to deduce the stochastic gradient algorithm based on filtering.In order to improve the parameter estimation of the algorithm,new interest length is introduced to expand the new interest vector into the new rate matrix and then multi-innovation extended stochastic gradient algorithm based on filtering is deduced.(2)For multivariate equation error auto regression systems,the appropriate filter is used to filter input and output data.Then the generalized stochastic gradient algorithm based on filtering and the multi-innovation generalized stochastic gradient algorithm can be deduced.In order to improve the precision of parameters estimation,all of the system data are be used at each step in the process of iterative calculation and gradient iteration algorithm based on filtering is deduced with the application of negative gradient search method further.The basic idea is the iterative parameter estimation in system model is calculated with noise estimate and the noise estimate is calculated with the last system iterative parameter estimate.(3)The above research results are further to be generalized to multivariate equation error moving average auto regression systems.The multivariable system disturbed by the colored noise contains a multivariable equation error moving average systems and a multivariable equation error auto regression equation error system.As aspecial case,a generalized extended stochastic gradient algorithm based on filtering,a multi-innovation generalized extended stochastic gradient algorithm based on filtering,a gradient iterative algorithm based on filtering and a limited amount of filter gradient iterative algorithm can be deduced.The proposed identification algorithms are tested by simulation examples,which test the effectiveness.In the last part of this paper,the advantages and disadvantages of the algorithms are analyzed and the application range is sure.The future research direction is clear.