Parameter identification of fractional-order Wiener system based on FF-ESG and GI algorithms

Fractional-order calculus has broad application scenarios in engineering and physics. Unlike integer-order calculus, fractional-order calculus has the ability to analyze nonclassical phenomena in science and engineering. For industrial processes with strong nonlinear characteristics, nonlinear models such as the Wiener model have become research hotspots. This paper studies the parameter identification of the fractional-order Wiener system. In this paper, the forgetting factor extended stochastic gradient (FF-ESG) algorithm and the gradient iterative (GI) algorithm are proposed to identify the parameters of the fractional-order Wiener system. Then, the convergence of the FF-ESG algorithm for the fractional-order Wiener system is analyzed. Both proposed algorithms can obtain exact parameter estimates, which are verified by a numerical example and a case study of a fluid control valve.