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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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
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Abstract 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.
AbstractList 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.
ArticleNumber 111913
Author Khan, Zeshan Aslam
Shah, Syed Muslim
Mehmood, Ammara
Chaudhary, Naveed Ishtiaq
Raja, Muhammad Asif Zahoor
Author_xml – sequence: 1
  givenname: Naveed Ishtiaq
  surname: Chaudhary
  fullname: Chaudhary, Naveed Ishtiaq
  organization: Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
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  givenname: Muhammad Asif Zahoor
  orcidid: 0000-0001-9953-822X
  surname: Raja
  fullname: Raja, Muhammad Asif Zahoor
  email: rajamaz@yuntech.edu.tw
  organization: Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, Taiwan
– sequence: 3
  givenname: Zeshan Aslam
  surname: Khan
  fullname: Khan, Zeshan Aslam
  email: zeeshan.aslam@iiu.edu.pk
  organization: Department of Electrical Engineering, International Islamic University, Islamabad, Pakistan
– sequence: 4
  givenname: Ammara
  surname: Mehmood
  fullname: Mehmood, Ammara
  email: ammara.mehmood@adelaide.edu.au
  organization: School of Electrical and Electronic Engineering, The University of Adelaide, Australia
– sequence: 5
  givenname: Syed Muslim
  surname: Shah
  fullname: Shah, Syed Muslim
  email: s.m.shah@ieee.org
  organization: Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan
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Hammerstein structure
Fractional calculus
Hierarchical identification
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Snippet The trend of developing fractional gradient based iterative adaptive strategies is evolved in the recent years through effectively exploring the fractional and...
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StartPage 111913
SubjectTerms Fractional calculus
Hammerstein structure
Hierarchical identification
Nonlinear systems
Title Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems
URI https://dx.doi.org/10.1016/j.chaos.2022.111913
Volume 157
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