Auxiliary Model Based Recursive Identification Methods And Convergence Analysis

The real industrial systems involve some measurable variables.However,there often exist many unavailable variables.This dissertation uses the auxiliary model to estimate the unmeasurable variables and studies the auxiliary model based recursive identification methods and analyzes the convergence for a class of multivariable output-error systems with unknown variables.The research has important theoretical significance and academic value.The main work is as follows.(1)For the multivariate output-error system with white noise,this dissertation studies the decomposition and auxiliary model based stochastic gradient algorithm and recursive least squares algorithm by using the auxiliary model identification idea and analyzes the convergence performance of the proposed algorithms by using the stochastic martingale theory.Further,for the multivariate output-error system with colored noise disturbing,this dissertation introduces a linear filter to pre-process the input/output data and studies the filtering based recursive identification algorithms.Filtering based algorithms can reduce the disturbance of the colored noise and improve the estimation accuracy.(2)For the multivariable Box-Jenkins-like system,the auxiliary model based hierarchical stochastic gradient algorithm and hierarchical least squares algorithm are derived to avoid redundant parameter estimates and to improve the computational efficiency,and the convergence is analyzed.To further improve the estimation accuracy,this dissertation designs a filter to transfer the identification system with colored noise into a system with white noise,and derives the filtering based auxiliary model hierarchical stochastic gradient algorithm and auxiliary model hierarchical least squares algorithm by using the filtered model.(3)For the nonlinear multivariable output-error-like system with known basis function,the main feature of such a nonlinear system is that it contains not only different types of parameters to be identified but also the parameter product of the linear part and nonlinear part.To solve this problem,the system is transferred into a bilinear-parameter model.By using the hierarchical identification theory,the obtained bilinear-parameter model is divided into three sub-systems,which involve the parameter vector/matrix belong to the linear part and the parameter vector belongs to the nonlinear part,respectively.Based on the sub-models,this dissertation interactively estimates the parameter vector/matrix in the sub-models by combining the auxiliary model idea with the negative gradient search and the least squares principle,and derives the auxiliary model based hierarchical stochastic gradient and hierarchical least squares algorithms which can improve the computational efficiency.This dissertation uses the Matlab simulation examples to verify the effectiveness of the studied algorithms and analyzes the convergence performance for several typical recursive estimation algorithms.