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

Naveed Ishtiaq Chaudhary, Muhammad Asif Zahoor Raja, Zeshan Aslam Khan, Khalid Mehmood Cheema and Ahmad H. Milyani
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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

Mathematics, 2021, vol. 9, issue 24, 1-14

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.

Keywords: fractional calculus; input nonlinear; nonlinear ARX systems; parameter estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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