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

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

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.

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  • Chaudhary, Naveed Ishtiaq & Raja, Muhammad Asif Zahoor & Khan, Zeshan Aslam & Mehmood, Ammara & Shah, Syed Muslim, 2022. "Design of fractional hierarchical gradient descent algorithm for parameter estimation of nonlinear control autoregressive systems," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922001230
    DOI: 10.1016/j.chaos.2022.111913
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    1. Mehmood, Khizer & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Cheema, Khalid Mehmood & Raja, Muhammad Asif Zahoor & Shu, Chi-Min, 2023. "Novel knacks of chaotic maps with Archimedes optimization paradigm for nonlinear ARX model identification with key term separation," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Naveed Ahmed Malik & Ching-Lung Chang & Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Chi-Min Shu & Sultan S. Alshamrani, 2022. "Knacks of Fractional Order Swarming Intelligence for Parameter Estimation of Harmonics in Electrical Systems," Mathematics, MDPI, vol. 10(9), pages 1-20, May.
    3. Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa Kausar & Raja, Muhammad Asif Zahoor & Chaudhary, Iqra Ishtiaq & Pinto, Carla M.A., 2022. "Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Khalid Mehmood Cheema & Muhammad Asif Zahoor Raja & Ahmad H. Milyani & Abdullah Ahmed Azhari, 2022. "Nonlinear Hammerstein System Identification: A Novel Application of Marine Predator Optimization Using the Key Term Separation Technique," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    5. Iman Faridmehr & Moncef L. Nehdi & Iraj Faraji Davoudkhani & Alireza Poolad, 2023. "Mountaineering Team-Based Optimization: A Novel Human-Based Metaheuristic Algorithm," Mathematics, MDPI, vol. 11(5), pages 1-36, March.
    6. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Zeshan Aslam Khan & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Ahmad H. Milyani, 2022. "Design of Aquila Optimization Heuristic for Identification of Control Autoregressive Systems," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    7. Khizer Mehmood & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Zeshan Aslam Khan & Muhammad Asif Zahoor Raja & Ahmad H. Milyani & Abdulellah Alsulami, 2023. "Design of Nonlinear Marine Predator Heuristics for Hammerstein Autoregressive Exogenous System Identification with Key-Term Separation," Mathematics, MDPI, vol. 11(11), pages 1-20, May.

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