Hierarchical Iterative Identification Methods For Multivariate Equation-Error Systems

System modeling and model identification are the basis of control system analysis and design,and the establishment of system mathematical model through measurement data is an effective means of in-depth study of the system.With the continuous improvement of the production technology of modern industrial system,the controlled object in the field of industrial control is often a multivariable system with large scale,complex structure and accompanied by uncertain interference.Therefore,how to apply the classical iterative class identification method to multivariable system identification has become a research hotspot in the field of system identification.Among the classical system identification methods,the iterative identification method can achieve higher parameter estimation accuracy,but when the dimensions of the unknown information matrix and parameter matrix are large,the traditional iterative identification method often fails to achieve better identification effect.Therefore,by combining the hierarchical identification principle,data filtering technology and multi-innovation identification theory with the iterative identification method,this paper studies the identification problem of multivariate equation-error systems under the interference of colored noises.The main research work of this paper is as follows.(1)Aiming at the multivariate equation-error system,the generalized iterative identification method of this type of system is proposed by applying the principle of negative gradient search and the principle of least squared.For the problem of identifying unknown items in the information matrix,the unknown items can be replaced with its previous step iterative estimates of the parameter,and the parameter estimation is refreshed with the replaced information matrix,so that batch data is used to realize the offline identification of parameter vectors.Further,the model decomposition technique and interactive estimation theory are used to study the multivariate hierarchical generalized iterative identification algorithm and hierarchical extended iterative identification algorithm,and analysis of the calculation amount of the algorithm proves that this method can effectively reduce the calculation amount of the algorithm,and the numerical simulation results further verify the effectiveness of the algorithm.(2)In the iterative identification method,in order to obtain good identification accuracy,we usually use batch data for identification,but this method is suitable for offline identification.In order to make the iterative identification method can be applied to the online identification,through a combination of multiple innovation identification theory,the generalized extended iterative identification algorithm for multivariate equation error autoregressive moving average systems is proposed.This iterative identification method uses the mobile data window to dynamically update the data in the data window,thereby improving the utilization rate of the observation data.(3)For the multivariate equation error system under the interference of colored noise,by using data filtering technology,a suitable filter is selected according to the noise model to filter the system observation data,and then the parameters of the system model and the noise model are interactively estimated,so as to propose a multivariate equation error system filter-based generalized extended iterative identification method.By introducing a linear filter into the original system model,the input and output data of the system are filtered,and then the filtered input and output data are used for identification,so as to effectively improve the parameter estimation accuracy.Numerical simulation results show that the filtering-based identification method has better convergence performance and higher parameter estimation accuracy when the noise variance is small.At the end of the paper,the work done in this topic is summarized,and some problems currently faced by multivariate system identification and the directions worthy of further research are introduced.