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Cited by 36Control Systems and IdentificationAdvanced Control Systems DesignStatistical and numerical algorithms

Parameter estimation of the fractional‐order Hammerstein–Wiener model using simplified refined instrumental variable fractional‐order continuous time

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Allafi, Walid, Zajic, Ivan, Uddin, Kotub, Burnham, Keith J.·2017·IET Control Theory & Applications
DOI 10.1049/iet-cta.2017.0284
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Abstract

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single‐input–single‐output fractional‐order continuous‐time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional‐order continuous‐time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non‐linearity of the Wiener model part does not need to be invertible. The input and output static non‐linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional‐order continuous‐time subsystem and the input and output static non‐linear functions from the sampled input–output data by considering the system to be a multi‐input–single‐output linear fractional‐order continuous‐time model. These extra inputs represent the basis functions of the static input and output non‐linearity, where the output basis functions are simulated according to the previous estimates of the fractional‐order linear subsystem and the static input non‐linear function at every iteration. It is also possible to estimate the classical integer‐order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer‐order continuous‐time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional‐order Hammerstein–Wiener output model.

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  • Allafi et al. [24] demonstrated identification of the fractional-order Hammerstein-Wiener model using a simplified refined instrumental variable method, considering some prior knowledge.

    “Allafi et al. [24] demonstrated the identification of the fractional-order Hammerstein-Wiener model using a simplified refined instrumental variable method, considering some prior knowledge.”

    From Application of Fractional Calculus for Parameter Estimation of Nonlinear Wiener Systems With Time Delay (2024) · cites this paper as [24]

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Authors
Allafi, W., Zajic, I., Uddin, K., & Burnham, K. J.
Affiliations
  • University of Warwick (GB)
  • School of Mechanical, Aerospace and Automotive Engineering Faculty of Engineering, Environment and Computing Coventry University 10 Coventry Innovation Village Coventry CV1 2TL United Kingdom
  • University of Wolverhampton (GB)
Corresponding author
Allafi, Walid
ORCID
Allafi, Walid
Venue
IET Control Theory & Applications
Publisher
Institution of Engineering and Technology (IET)
Published
2017-08-09
Volume
11
Issue
15
Pages
2591-2598
ISSN
  • 1751-8644 (ISSN-L)
  • 1751-8652
DOI
10.1049/iet-cta.2017.0284
OpenAlex
W2731460934
Cited by
36
References
0
Citations by year
2026: 5 · 2025: 4 · 2024: 5 · 2023: 2 · 2022: 1 · 2021: 3 · 2020: 5 · 2019: 5 · 2018: 6
FWCI
2.74
Type
journal article
Language
en
Open access
Licence
Locations
  • IET Control Theory and Applications (publishedVersion, cc-by)
  • Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
  • Wolverhampton Intellectual Repository and E-Theses (University of Wolverhampton) (submittedVersion, cc-by)
Funders
Engineering and Physical Sciences Research Council (EP/M507143/1, EP/N001745/1)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
Keywords
parameter estimation, nonlinear system identification, static nonlinearity, basis function expansion, input-output data

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