Nonlinear system identification of fractional Wiener models

Sersour, Lamia; Djamah, Tounsia; Bettayeb, Maâmar

doi:10.1007/s11071-018-4142-0

Cited by 27 publications

(9 citation statements)

References 29 publications

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“…By successive -order differentiating (19), it can be seen that, with d 1 = 1, u a i and a i (i ∈ {1, … , n}) given in (11) and (12), respectively, satisfy (19). By substituting (19) into (18) and following the similar procedure as that used in obtaining (18) from (16), it can be seen that a state-space realization of (18) is as follows:…”

Section: Identification Algorithmmentioning

confidence: 99%

“…In this situation, which is the case considered in this paper, the state‐space identification becomes difficult because it includes the estimation of not only the unknown parameters but also the unknown states. It is noteworthy that two main strategies have been presented in the literature on Hammerstein state‐space identification: (i) identification algorithms that are under the assumption of the system states being known and (ii) hierarchical methods based on the cost function minimization problem, which commonly bring the system back to its discrete‐time input‐output representation . Recently, the authors proposed an observer‐based state‐space identification using an auxiliary model‐based observer .…”

Section: Introductionmentioning

confidence: 99%

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Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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Summary This paper introduces a multiple‐input–single‐output (MISO) neuro‐fractional‐order Hammerstein (NFH) model with a Lyapunov‐based identification method, which is robust in the presence of outliers. The proposed model is composed of a multiple‐input–multiple‐output radial basis function neural network in series with a MISO linear fractional‐order system. The state‐space matrices of the NFH are identified in the time domain via the Lyapunov stability theory using input‐output data acquired from the system. In this regard, the need for the system state variables is eliminated by introducing the auxiliary input‐output filtered signals into the identification laws. Moreover, since practical measurement data may contain outliers, which degrade performance of the identification methods (eg, least‐square–based methods), a Gaussian Lyapunov function is proposed, which is rather insensitive to outliers compared with commonly used quadratic Lyapunov function. In addition, stability and convergence analysis of the presented method is provided. Comparative example verifies superior performance of the proposed method as compared with the algorithm based on the quadratic Lyapunov function and a recently developed input‐output regression‐based robust identification algorithm.

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Section: Identification Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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“…e authors in [28] have proposed a bias compensated method for system identification of the fractional closed-loop system. In 2018, the nonlinear system identification of fractional Wiener models has been established by Sersour et al [29]. Very recently, in 2020-2021, the fractional order system identification has attracted more and more attention: In [30] the authors have proposed an output error-based method to identify multi input single output (MISO) systems using fractional models.…”

Section: Introductionmentioning

confidence: 99%

A Bias-Corrected Method for Fractional Linear Parameter Varying Systems

Yakoub

Naifar

Amairi

et al. 2022

Mathematical Problems in Engineering

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This paper proposes an identification algorithm for the fractional Linear Parameter Varying (LPV) system considering noisy scheduling and output measurements. A bias correction technique is provided in order to compensate for the bias caused by the least squares algorithm. This approach was created to estimate either coefficients or fractional-order differentiation, and it has been proven to produce unbiased and reliable results. The suggested method’s performance is assessed by the identification of two fractional models and was compared with Nelder–Mead Simplex method.

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“…In industrial production, such as chemical processes, communication systems, biological processes and so on, many components of the system have nonlinear characteristics, 1,2 which lead to the study of nonlinear systems complicate but more meaningful. Therefore, the identification of nonlinear systems has been widely concerned by experts at home and abroad 3,4 . By observing the input and output data to identify the system, the mathematical model of the system can be obtained, which is beneficial to predictive control, 5 state estimation, 6 and fault detection 7 .…”

Section: Introductionmentioning

confidence: 99%

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

Jin

Wang

Cai

et al. 2021

Adaptive Control & Signal

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Summary In this paper, the parameter estimation issue of Wiener system with random time delay and missing output data is studied. The linear part of Wiener system is described by Finite Impulse Response (FIR) model. The mathematical formula of the Expectation Maximum algorithm to identify Wiener‐FIR system that contains the random time delay and the nonlinear output data in missing completely at random mechanism is derived, which is never considered before. To obtain the unmeasurable intermediate variable in Wiener‐FIR system, the idea of auxiliary model is adopted. The time delay and system parameters can be estimated simultaneously by this method. Numerical example and the identification of water tank system example are carried out, the effectiveness of the algorithm is proved.

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Nonlinear system identification of fractional Wiener models

Cited by 27 publications

References 29 publications

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

A Bias-Corrected Method for Fractional Linear Parameter Varying Systems

Parameter identification for Wiener‐finite impulse response system with output data of missing completely at random mechanism and time delay

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