Recursive Identification Algorithms And Convergence Analysis For Feedback Nonlinear Equation-Error Systems

The feedback nonlinear systems exist widely in industrial production process,which consist of the dynamic linear subsystems of the forward channels and the static nonlinearities of the feedback channels.And they are the typical block-oriented nonlinear systems.Linear system identification has become mature and how to apply linear system identification methods to nonlinear system identification has become a research hotspot.The common model structure includes the equation error model and output error model.This paper investigates the recursive identification algorithms of the feedback nonlinear equation-error systems,which is meaningful and valuable in theory.Moreover,combined with the stochastic process theory,the convergence theorems of the proposed algorithms are analyzed.The main contents are as follows.1.Through the parameterization,the bilinear-parameter identification models of the feedback nonlinear equation-error moving average systems are obtained.It is noted that the product terms of the parameter vectors exist in the identification model,which presents some challenges and issues to us.The original identification model can be transformed into a pseudo-linear regression model with parameters to be identified in the information vector.Then,a recursive extended least squares(RELS)algorithm and an extended stochastic gradient(ESG)algorithm are developed.2.In order to improve the computational efficiency,the hierarchical identification principle and the decomposition technology are employed to decompose the product terms.The original identification model is transformed into three sub-models for identification and a hierarchical extended least squares(HELS)algorithm is proposed to identify the feedback nonlinear equation-error moving average systems.Furthermore,the multi-innovation theory is applied to estimate the feedback nonlinear systems to improve the estimation accuracy.Introducing the innovation length,the scalar innovation is expanded to the innovation vector and a multi-innovation extended stochastic gradient(MI-ESG)algorithm is presented.3.For identifying the feedback nonlinear equation-error autoregressive moving average systems,a recursive generalized extended least squares(RGELS)algorithm and a generalized extended stochastic gradient(GESG)algorithm are discussed.In order to reduce the impact of colored noises on the parameter estimation accuracy,the data filtering technology is applied to transform the feedback nonlinear systems interfered by colored noises into those interfered by white noises.A filtered recursive generalized extended least squares(F-RGELS)algorithm and a filtered generalized extended stochastic gradient(F-GESG)algorithm are deduced.4.The convergence theorems of the proposed algorithms are analyzed by virtue of the stochastic process theory and the proper persistent excitation conditions.The simulation experiments are provided to indicate the effectiveness of the proposed algorithms from the aspects of the parameter estimation and the model validation.Meanwhile,the computational cost of some proposed algorithms are also compared and analyzed in this paper.