Parameter Estimation of Fractional Wiener Systems with the Application of Photovoltaic Cell Models

Ce Zhang (), Xiangxiang Meng and Yan Ji
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Ce Zhang: Yantai Vocational College, Yantai 264670, China
Xiangxiang Meng: College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China
Yan Ji: College of Automation and Electronic Engineering, Qingdao University of Science and Technology, Qingdao 266061, China

Mathematics, 2023, vol. 11, issue 13, 1-22

Abstract: Fractional differential equations are used to construct mathematical models and can describe the characteristics of real systems. In this paper, the parameter estimation problem of a fractional Wiener system is studied by designing linear filters which can obtain smaller tunable parameters and maintain the stability of the parameters in any case. To improve the identification performance of the stochastic gradient algorithm, this paper derives two modified stochastic gradient algorithms for the fractional nonlinear Wiener systems with colored noise. By introducing the forgetting factor, a forgetting factor stochastic gradient algorithm is deduced to improve the convergence rate. To achieve more efficient and accurate algorithms, we propose a multi-innovation forgetting factor stochastic gradient algorithm by means of the multi-innovation theory, which expands the scalar innovation into the innovation vector. To test the developed algorithms, a fractional-order dynamic photovoltaic model is employed in the simulation, and the dynamic elements of this photovoltaic model are estimated using the modified algorithms. Concurrently, a numerical example is given, and the simulation results verify the feasibility and effectiveness of the proposed procedures.

Keywords: gradient search; forgetting factor; multi-innovation theory; fractional-order system; dynamic photovoltaic model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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