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

Naveed Ishtiaq Chaudhary, Muhammad Asif Zahoor Raja, Zeshan Aslam Khan, Ammara Mehmood and Syed Muslim Shah

Chaos, Solitons & Fractals, 2022, vol. 157, issue C

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.

Keywords: Nonlinear systems; Hammerstein structure; Fractional calculus; Hierarchical identification (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001230

DOI: 10.1016/j.chaos.2022.111913

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