Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems

The trend of developing fractional gradient based iterative adaptive strategies is evolved in the recent years through effectively exploring the fractional and fractal dynamics. In this study, fractional hierarchical gradient descent (FHGD) is proposed by generalizing the standard hierarchical gradi...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 157; p. 111913
Main Authors: Chaudhary, Naveed Ishtiaq, Raja, Muhammad Asif Zahoor, Khan, Zeshan Aslam, Mehmood, Ammara, Shah, Syed Muslim
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2022
Subjects:
Fractional calculus
Hammerstein structure
Hierarchical identification
Nonlinear systems
Nonlinear systems
Hammerstein structure
Fractional calculus
Hierarchical identification
ISSN:0960-0779, 1873-2887
Online Access:Get full text
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Summary:The trend of developing fractional gradient based iterative adaptive strategies is evolved in the recent years through effectively exploring the fractional and fractal dynamics. In this study, fractional hierarchical gradient descent (FHGD) is proposed by generalizing the standard hierarchical gradient descent (HGD) to fractional order for effectively solving nonlinear system identification problem. The FHGD is effectively to applied to estimate the parameters of nonlinear control autoregressive (NCAR) systems under different fractional order and noise conditions. The fractional order greater than 1 provides faster convergence speed, less than 1 gives better steady state performance and equal to 1 reduces the FHGD to HGD. The accurate estimation of NCAR system parameters representing electrically stimulated muscle model validates the efficacy and robustness of the proposed FHGD in comparison with the standard HGD.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.111913