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Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle

Author

Listed:
  • Naveed Ishtiaq Chaudhary

    (Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan)

  • Muhammad Asif Zahoor Raja

    (Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou 64002, Taiwan)

  • Zeshan Aslam Khan

    (Department of Electrical Engineering, International Islamic University, Islamabad 44000, Pakistan)

  • Khalid Mehmood Cheema

    (School of Electrical Engineering, Southeast University, Nanjing 210096, China)

  • Ahmad H. Milyani

    (Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

Recently, a quasi-fractional order gradient descent (QFGD) algorithm was proposed and successfully applied to solve system identification problem. The QFGD suffers from the overparameterization problem and results in estimating the redundant parameters instead of identifying only the actual parameters of the system. This study develops a novel hierarchical QFDS (HQFGD) algorithm by introducing the concepts of hierarchical identification principle and key term separation idea. The proposed HQFGD is effectively applied to solve the parameter estimation problem of input nonlinear autoregressive with exogeneous noise (INARX) system. A detailed investigation about the performance of HQFGD is conducted under different disturbance conditions considering different fractional orders and learning rate variations. The simulation results validate the better performance of the HQFGD over the standard counterpart in terms of estimation accuracy, convergence speed and robustness.

Suggested Citation

  • Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Zeshan Aslam Khan & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Hierarchical Quasi-Fractional Gradient Descent Method for Parameter Estimation of Nonlinear ARX Systems Using Key Term Separation Principle," Mathematics, MDPI, vol. 9(24), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3302-:d:705678
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    References listed on IDEAS

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    1. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. 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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    Citations

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    Cited by:

    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. Faisal Altaf & Ching-Lung Chang & Naveed Ishtiaq Chaudhary & Muhammad Asif Zahoor Raja & Khalid Mehmood Cheema & Chi-Min Shu & Ahmad H. Milyani, 2022. "Adaptive Evolutionary Computation for Nonlinear Hammerstein Control Autoregressive Systems with Key Term Separation Principle," Mathematics, MDPI, vol. 10(6), pages 1-20, March.
    4. 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.
    5. Malik, Muhammad Faizan & Chang, Ching-Lung & Chaudhary, Naveed Ishtiaq & Khan, Zeshan Aslam & Kiani, Adiqa kausar & Shu, Chi-Min & Raja, Muhammad Asif Zahoor, 2023. "Swarming intelligence heuristics for fractional nonlinear autoregressive exogenous noise systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. 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).

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