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Identification Methods for a Class of Nonlinear Systems

Author: ChenJing
Tutor: DingFeng
School: Jiangnan University
Course: Control Theory and Control Engineering
Keywords: stochastic gradient iterative algorithm least squares key term separation principle nonlinear systems
CLC: TP13
Type: PhD thesis
Year: 2013
Downloads: 114
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Abstract


Due to hardware limitations and environmental impacts, nonlinear systems are wide-ly found in process control feld. Nonlinear system identifcation constitutes a crucial partin control designs if the parameters of the nonlinear systems are unknown. Since non-linear systems have complex structures, coupling characteristics and large dimension ofunknown parameters, the traditional identifcation methods for linear systems cannot beapplied for nonlinear systems directly. Therefore, the study of identifcation methods fornonlinear systems is of universal signifcance and has wide application prospects. By usingthe auxiliary model, the key term separation principle and the Weierstrass approxima-tion theorem, this dissertation aims to develop new identifcation methods for nonlinearsystems, and the performances of the methods are illustrated by computer simulations.The main contributions are summarized as follows.(1) For the nonlinear systems with polynomial nonlinearity, an auxiliary model basedgeneralized extended stochastic gradient (SG) algorithm is developed by using theauxiliary model and the multi-innovation theory. The outputs of the auxiliary modelcan replace the unknown inner variables and the multi-innovation method can im-prove the accuracy of parameter estimation. Furthermore, this method is extendedto identify multivariable nonlinear systems.(2) Based on the key term separation principle, an SG algorithm is derived for nonlin-ear systems with preload nonlinearity, and a polynomial transformation techniquebased SG algorithm and a missing output estimation model based SG algorithm areproposed for dual-rate nonlinear systems with preload nonlinearity. Compared withthe polynomial transformation technique based SG algorithm, the missing outputestimation model based SG algorithm can directly estimate the parameters of thedual-rate systems and not increase the number of the unknown parameters.(3) For the nonlinear systems with known hard nonlinearities, the key term separationprinciple based GI algorithm is derived. Compared with the on-line algorithms, theGI algorithm is efective in dealing with nonlinear systems which contain unknowninner variables. Furthermore, based on the Weierstrass approximation theorem, amodifed SG (M-SG) algorithm and a forgetting factor SG (FF-SG) algorithm areproposed for nonlinear systems with unknown hard nonlinearities.(4) For a nonlinear membership function, two model transformation based estimationmethods are proposed. The proposed methods can greatly save the computational cost by using the model transformation technique. Furthermore, an FF-SG algorith-m and an M-SG algorithm are proposed for the polynomial function of the Weier-strass approximation theorem, and the proposed methods have quick convergencerate and low computational load.

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