Identification Methods For Wiener Nonlinear Systems

Wiener nonlinear systems are typical block-oriented nonlinear systems and are widelyfound in the feld of industrial process control. However, the coupling characteristics andthe large number of variables result in the complex structure of Wiener nonlinear systems.The traditional identifcation methods can not be applied in Wiener nonlinear systems.This dissertation aims to develop identifcation methods for Wiener nonlinear systems,and the performances of the methods are illustrated by data simulations. Therefore, thestudy of identifcation methods for Wiener nonlinear systems is of universal signifcanceand has wide application prospects. The main contributions are summarized as follows.①The Wiener nonlinear model contains a linear dynamic subsystem and a staticnonlinear subsystem. There exists a difculty that the intermediate variables (i.e. thelinear dynamic subsystem output) is unmeasured. Based on the auxiliary model and thehierarchical identifcation concept, the gradient iterative algorithm and least-squares iter-ative algorithm are proposed by using the output of the auxiliary model as the estimatesof the unmeasured intermediate variables.②For Wiener nonlinear systems disturbed by colored noises, the information matrixcontains the unmeasured noise variables. The Newton iterative algorithms are derived bymeans of the auxiliary model estimating the unmeasured intermediate variables. As theHessian matrix is not a positive defnite matrix, the direction can not be guaranteed tobe descent direction generated in the objective function. If the Hessian matrix is singular,the Newton iterative algorithm can not be performed. To overcome two shortcomings,the quasi-Newton iterative algorithm is presented for Wiener nonlinear systems disturbedby colored noises.③The gradient iterative algorithm is derived for Wiener nonlinear output errormodel with non-uniform sampling. To improve the convergence rate of the gradientiterative algorithm, the conjugate gradient iterative algorithm is developed for Wienernonlinear output error model with non-uniform sampling. The basic idea is, by meansof the hierarchical identifcation principle and the auxiliary model, to estimate the inter-mediate unknown variables. The conjugate gradient iterative algorithm has superlinearconvergence rate to be superior to the gradient iterative algorithm.④For the multiple-input Wiener nonlinear model, there are more estimated param-eters and more complex structure than the single-input one. The Levenberg-Marquardtiterative algorithm is proposed in order to improve the accuracy and convergence rate. Byadjusting the damping coefcient in the certain updating rules, the Levenberg-Marquardtiterative algorithm can not only converge globally as the gradient iterative algorithm, but also converge rapidly as the Newton iterative algorithm. For multiple-input single-outputWiener nonlinear systems with invertible polynomial nonlinearities, the gradient iterativealgorithm is derived and then applied to model the glutamate fermentation process.