Maximum Likelihood Recursive Identification For Multivariate Equation-error Systems

In the actual industrial process,multivariable systems with complex structures exist widely.Therefore,the identification of multivariable systems has always been a hot and difficult topic in the field of control theory.As an estimation method based on probability,the maximum likelihood estimator has good statistical properties and is widely used in many fields.This thesis considers the maximum likelihood identification problems for the mutivariate equation-error systems with colored noise by combining the maximum likelihood principle with the recursive identification theory.The major results are as follows.1.For the multivariate equation-error moving average systems,the system contains both parameter vectors and parameter matrices.The system is decomposed into subsystems containing only parameter vectors.The subsystem identification model is obtained by defining the subsystem parameter vectors and the subsystem information vectors.The maximum likelihood extended stochastic gradient identification algorithm is derived for the subsystems.In order to improve the convergence speed and parameter estimation accuracy of the algorithm,a maximum likelihood multiinnovation extended stochastic gradient identification algorithm and a multivariate maximum likelihood recursive extended least squares algorithm are derived.2.For the multivariate equation-error autoregressive systems,the system is decomposed into multiple subsystems with multiple inputs and single outputs.All subsystems contain coupled parameter vectors.In order to coordinate the coupling relationship of parameter vectors between subsystems and to improve the accuracy of parameter estimation,the concept of coupling identification is introduced.A coupled maximum likelihood recursive generalized least squares algorithm and a coupled maximum likelihood generalized stochastic gradient algorithm are derived.In order to improve the parameter estimation accuracy of the gradient algorithm,a coupled maximum likelihood multi-innovation generalized stochastic gradient identification algorithm is derived by introducing the multi-innovation.3.For the multivariate equation-error autoregressive moving average systems,the noise structure of the system is complex.There are many parameters to be identified.In order to reduce the influence of the colored noise on parameter estimation,the data filtering technique is used.A filtering-based maximum likelihood recursive extended least squares algorithm and a filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm are proposed.The proposed identification algorithms are simulated numerically to verify the effectiveness of the algorithms.The simulation results show that the multivariate maximum likelihood recursive extended least squares algorithm has high estimation accuracy.The coupled maximum likelihood multi-innovation generalized stochastic gradient identification algorithm can effectively improve the convergence speed and parameter estimation accuracy of the gradient algorithm.The filtering-based maximum likelihood recursive extended least squares algorithm can effectively improve the accuracy of parameter estimation.