Frequency domain identification of hammerstein models

Bai, Er‐Wei

doi:10.1109/tac.2003.809803

Cited by 110 publications

(3 citation statements)

References 20 publications

(25 reference statements)

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“…On the one hand,ũ is the Gaussian functions vector, which implies that it has infinite number of sinusoidal signals of distinct frequencies even if input u is a sinusoidal signal vector. 53 On the other hand, when is set to one, which is the worst case, it is deduced from (31) thatũ must have at least (2n + 1)/2 distinct frequencies to be not the solution of (31). Thus,ũ cannot be a solution of (31) for every sinusoidal input u.…”

Section: Corollarymentioning

confidence: 99%

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: Corollarymentioning

confidence: 99%

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Rahmani

Farrokhi

2019

Intl J Robust & Nonlinear

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“…However, much research works remain to be done for realization on nonlinear mathematical models that accurately represent these processes [1][2][3][4]. One way to cope with this difficulty is to use the block-oriented nonlinear models [5][6][7], which represent a combination of static nonlinear components and linear dynamic submodels.…”

Section: Introductionmentioning

confidence: 99%

Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

2021

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This paper presents the problem of robust and nonfragile stabilization of nonlinear systems described by multivariable Hammerstein models. The objective is focused on the design of a nonfragile feedback controller such that the resulting closed-loop system is globally asymptotically stable with robust H ∞ disturbance attenuation in spite of controller gain variations. First, the parameters of linear and nonlinear blocks characterizing the multivariable Hammerstein model structure are separately estimated by using a subspace identification algorithm. Second, approximate inverse nonlinear functions of polynomial form are proposed to deal with nonbijective invertible nonlinearities. Thereafter, the Takagi–Sugeno model representation is used to decompose the composition of the static nonlinearities and their approximate inverses in series with the linear subspace dynamic submodel into linear fuzzy parts. Besides, sufficient stability conditions for the robust and nonfragile controller synthesis based on quadratic Lyapunov function, H ∞ criterion, and linear matrix inequality approach are provided. Finally, a numerical example based on twin rotor multi-input multi-output system is considered to demonstrate the effectiveness.

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“…Most recently, the Hammerstein structure was used to describe the electrical muscle stimulation models which play an important role in restoring functionality of paralyzed muscles [2]. Some existing estimation approaches of Hammerstein systems are based on iterative methods using least squares [3], relay feedback [4,5], the over-parameterization method [6] and the frequency domain method [7]. The concept of separating the identification problem of the nonlinear static function from the linear subsystem in a Hammerstein model by using a special test signal was first proposed by Sung [8] and later extended to Hammerstein-Wiener models [9].…”

Section: Introductionmentioning

confidence: 99%

Parametric Identification of Nonlinear Fractional Hammerstein Models

2019

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In this paper, a system identification method for continuous fractional-order Hammerstein models is proposed. A block structured nonlinear system constituting a static nonlinear block followed by a fractional-order linear dynamic system is considered. The fractional differential operator is represented through the generalized operational matrix of block pulse functions to reduce computational complexity. A special test signal is developed to isolate the identification of the nonlinear static function from that of the fractional-order linear dynamic system. The merit of the proposed technique is indicated by concurrent identification of the fractional order with linear system coefficients, algebraic representation of the immeasurable nonlinear static function output, and permitting use of non-iterative procedures for identification of the nonlinearity. The efficacy of the proposed method is exhibited through simulation at various signal-to-noise ratios.

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Frequency domain identification of hammerstein models

Cited by 110 publications

References 20 publications

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

Parametric Identification of Nonlinear Fractional Hammerstein Models

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Frequency domain identification of hammerstein models

Cited by 110 publications

References 20 publications

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Robust identification of MISO neuro‐fractional‐order Hammerstein systems

Nonfragile H ∞ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models

Parametric Identification of Nonlinear Fractional Hammerstein Models

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Nonfragile $H_{\infty}$ Stabilizing Nonlinear Systems Described by Multivariable Hammerstein Models