Some Stochastic Gradient Algorithms for Hammerstein Systems with Piecewise Linearity

Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed...

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Bibliographic Details
Published in:Circuits, systems, and signal processing Vol. 40; no. 4; pp. 1635 - 1651
Main Authors: Pu, Yan, Yang, Yongqing, Chen, Jing
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2021
Springer Nature B.V
Subjects:
Algorithms
Circuits and Systems
Electrical Engineering
Electronics and Microelectronics
Engineering
Instrumentation
Linearity
Regression models
Signal,Image and Speech Processing
Gradient search
Parameter estimation
Aitken method
Forgetting factor
Piecewise linearity
ISSN:0278-081X, 1531-5878
Online Access:Get full text
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Summary:Some stochastic gradient (SG) algorithms for Hammerstein systems with piecewise linearity are developed in this paper. Due to the complexity of the nonlinear structure, the key term separation is used to transfer the nonlinear model into a regression model, and then, some SG algorithms are proposed for this model. Since the SG algorithm has slow convergence rate, a forgetting factor SG algorithm and an Aitken SG algorithm are provided. Compared with the forgetting factor SG algorithm, the Aitken SG algorithm has smaller variance of estimation error, which means the Aitken SG algorithm is more effective. Two simulation examples are provided to show the effectiveness of the proposed algorithms.
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ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-020-01554-z