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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. Atangana, Abdon & Shafiq, Anum, 2019. "Differential and integral operators with constant fractional order and variable fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 226-243.
    2. Ghanbari, Behzad & Atangana, Abdon, 2020. "A new application of fractional Atangana–Baleanu derivatives: Designing ABC-fractional masks in image processing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    4. Qureshi, Sania & Atangana, Abdon, 2020. "Fractal-fractional differentiation for the modeling and mathematical analysis of nonlinear diarrhea transmission dynamics under the use of real data," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    5. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
    6. Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    9. Zeshan Aslam Khan & Naveed Ishtiaq Chaudhary & Syed Zubair, 2019. "Fractional stochastic gradient descent for recommender systems," Electronic Markets, Springer;IIM University of St. Gallen, vol. 29(2), pages 275-285, June.
    10. Zaer Abo-Hammour & Omar Abu Arqub & Shaher Momani & Nabil Shawagfeh, 2014. "Optimization Solution of Troesch’s and Bratu’s Problems of Ordinary Type Using Novel Continuous Genetic Algorithm," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-15, February.
    11. Omar Abu Arqub & Zaer Abo-Hammour & Shaher Momani & Nabil Shawagfeh, 2012. "Solving Singular Two-Point Boundary Value Problems Using Continuous Genetic Algorithm," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-25, November.
    12. Heydari, M.H. & Atangana, A., 2019. "A cardinal approach for nonlinear variable-order time fractional Schrödinger equation defined by Atangana–Baleanu–Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 339-348.
    13. Santanu Saha Ray & Abdon Atangana & S. C. Oukouomi Noutchie & Muhammet Kurulay & Necdet Bildik & Adem Kilicman, 2014. "Fractional Calculus and Its Applications in Applied Mathematics and Other Sciences," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-2, December.
    14. Chen, Yuquan & Gao, Qing & Wei, Yiheng & Wang, Yong, 2017. "Study on fractional order gradient methods," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 310-321.
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    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. Xu, Huan & Xu, Ling & Shen, Shaobo, 2024. "Online identification methods for a class of Hammerstein nonlinear systems using the adaptive particle filtering," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    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. 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).
    8. Khan, Taimoor Ali & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Mehmood, Khizer & Hsu, Chung-Chian & Raja, Muhammad Asif Zahoor, 2024. "Design of Runge-Kutta optimization for fractional input nonlinear autoregressive exogenous system identification with key-term separation," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    9. 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.
    10. Mukhtar, Roshana & Chang, Chuan-Yu & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Shu, Chi-Min, 2024. "Novel nonlinear fractional order Parkinson's disease model for brain electrical activity rhythms: Intelligent adaptive Bayesian networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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