Abstract:This paper presents an auxiliary model (AM) based stochastic gradient (SG) algorithm,an AM multi-innovation SG algorithm and an AM recursive least squares algorithm for autoregressive output-error systems and presents a filtering based AM generalized extended SG algorithm,a filtering based AM multi-innovation generalized extended SG algorithm and a filtering based AM recursive generalized extended least squares algorithm for autoregressive output-error autoregressive moving average (AR-OEARMA) systems,namely autoregressive Box-Jenkins systems.

Abstract:For input nonlinear output-error systems with known bases,this paper presents the over-parameterization model based auxiliary model (AM) recursive identification methods,the over-parameterization model based AM hierarchical identification methods,the key term separation based AM recursive identification methods,the key term separation based AM two-stage recursive identification methods,the key term separation based AM three-stage recursive identification methods,the bilinear-in-parameter model decomposition based AM stochastic gradient identification methods and the bilinear-in-parameter model decomposition based AM recursive least squares identification methods.Finally,the computational efficiency and the computational steps of several typical identification algorithms are discussed.The convergence of the proposed algorithms needs further study.

Abstract:The input nonlinear systems include the input nonlinear equation-error type systems and the input nonlinear output-error type systems.According to the over-parameterization model,the key term separation and the data filtering,this paper studies and presents the over-parameterization model based auxiliary model recursive identification (AM-RI) methods,the key term separation based AM-RI methods and the data filtering based AM-RI methods for input nonlinear output-error autoregressive systems.These methods can be extended to other input nonlinear output-error systems,output nonlinear output-error type systems and feedback nonlinear systems.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.

Abstract:The auxiliary model identification idea is presented for the systems with unmeasurable variables.It is an important method for studying the system identification with unknown variables.Introducing the auxiliary model identification idea and taking the input nonlinear finite impulse response system with white noise as an example,this paper studies the auxiliary model (AM) based gradient identification algorithms,the AM multi-innovation gradient identification algorithms,the interval-varying AM multi-innovation gradient identification algorithms;the interval-equating AM gradient identification algorithms and the interval-equating AM multi-innovation gradient identification algorithms.

Abstract:For input nonlinear finite impulse response systems,based on the auxiliary model identification idea,this paper studies the auxiliary model (AM) based least squares (LS) identification algorithms,the AM multi-innovation LS identification algorithms,the interval-varying AM LS identification algorithms,the interval-varying AM multi-innovation LS identification algorithms and the AM finite data window LS identification algorithms,including the weighted LS algorithms and the forgetting factor LS algorithms.

Abstract:Performance analysis of identification methods is the important and difficult projects in the area of system identification.Once one new identification method is born,its convergence analysis appears.The auxiliary model identification is a branch of system identification and has become a large family of identification methods,their convergence brings many projects.This paper studies the consistent convergence of the auxiliary model (AM) based stochastic gradient (SG) algorithm,the AM recursive least squares (RLS) algorithm,the AM multi-innovation SG algorithm,the interval-varying AM SG algorithm and the interval-varying AM RLS algorithm for output-error systems,and analyzes approximately the convergence of the AM recursive generalized extended least squares algorithm for Box-Jenkins systems.

Abstract:Typical block-oriented structure nonlinear systems include the basic input nonlinear systems,the output nonlinear systems,the input-output nonlinear systems and the feedback nonlinear systems.The input nonlinear systems include the input nonlinear equation-error type systems and the input nonlinear output-error type systems.Taking the input nonlinear equation-error autoregressive systems (namely the input nonlinear controlled autoregressive autoregressive (IN-CARAR) systems as an example,this paper studies and presents stochastic gradient (SG) identification methods,multi-innovation SG methods,recursive least squares (LS) identification methods and multi-innovation LS identification methods for IN-CARAR systems based on the over-parameterization model,the key term separation principle and the data filtering technique,the model decomposition technique.These methods can be extended to other input nonlinear equation-error systems,input nonlinear output-error type systems,output nonlinear equation-error type systems and output nonlinear output-error systems,and feedback nonlinear systems.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.

Abstract:For input nonlinear equation-error systems (namely the input nonlinear controlled autoregressive (IN-CAR) systems),this paper studies and presents the over-parameterization model based multi-innovation identification (MI) methods,the over-parameterization model based hierarchical MI methods and the key term separation based MI methods,and uses the decomposition technique to present the key term separation based two-stage MI methods and the key term separation based three-stage MI methods.These methods can be extended to other input nonlinear equation-error systems,input nonlinear output-error type systems,output nonlinear equation-error type systems and output nonlinear output-error systems,and feedback nonlinear systems.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.

Abstract:With the development of control technology,the scales of the control systems become larger and larger,so does the computational load of the identification algorithms.For nonlinear systems with complex structures,especially for the nonlinear systems that contain the products of the unknown parameters of the nonlinear part and linear part,the sizes of the involved matrices in the over-parameterization model based least squares methods greatly increase,this makes the computational amount of the identification algorithms increase dramatically.Therefore,it is necessary to explore new parameter estimation methods with less computation.For output nonlinear equation-error type systems,this paper discusses the over-parameterization model based recursive least squares type identification algorithms; in order to reduce computational loads and improve the identification accuracy,this paper uses the decomposition technique and the filtering technique and presents the model decomposition based recursive least squares identification methods and the filtering based recursive least squares identification methods.Finally,the computational efficiency,the computational steps and the flowcharts of several typical identification algorithms are discussed.

Abstract:Systems have two categories, one is linear and the other is nonlinear.The linear systems have uniform descriptions and the nonlinear systems have countless categories and have no uniform descriptions.The linear-parameter systems are a special class of nonlinear systems and are linear on the parameter space.For pseudo-linear-parameter systems, this paper studies and presents the auxiliary model based multi-innovation(MI) identification methods, the data filtering based auxiliary model MI identification methods, the model decomposition based auxiliary model MI identification methods, and the filtering based decomposition MI identification methods.Finally, the computational efficiency, the computational steps and the flowcharts of several typical identification algorithms are discussed.