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Fitting the Nonlinear Systems Based on the Kernel Functions Through Recursive Search

Jimei Li, Yingjiao Rong, Cheng Wang*, Feng Ding, and Xiangli Li
International Journal of Control, Automation, and Systems, vol. 20, no. 6, pp.1849-1860, 2022

Abstract : Membership function identification is an important part of studying fuzzy control theory. Gaussian membership functions are widely used in the defuzzification processes, while the simple fuzzy processing reduces the dynamic characteristics of models. In order to reflect the dynamic performance of the nonlinear systems accurately, this paper introduces the idea of the multi-model control and fits a kernel function for the defuzzification processes by selecting the scheduling modes. Based on the gradient search, we present a least mean square (LMS) algorithm to solve the parameter estimation problem of the nonlinear systems. Considering the difficulty of determining the step sizes in the LMS algorithm, an overall stochastic gradient (O-SG) algorithm is deduced to obtain the optimal step size and estimate the unknown parameters. In order to improve the estimation accuracy, we introduce a forgetting factor into the O-SG algorithm to obtain the overall forgetting factor stochastic gradient (O-FFSG) algorithm. With the appropriate forgetting factors, the O-FFSG algorithm can effectively used for identifying the nonlinear systems. The performances of the proposed algorithms are tested by a numerical example.

Keyword : Gradient search, membership function, multi-model control, nonlinear system, parameter estimation.

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