Recursive prediction error identification of fractional order models

Djouambi, Abdelbaki; Voda, Alina; Charef, Abdelfatah

doi:10.1016/j.cnsns.2011.08.015

Cited by 42 publications

(11 citation statements)

References 6 publications

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“…) denotes Euler's Gamma function, with the following definition:

normalΓ ((), n) = \int_{0}^{\infty} t^{n - 1} e^{- t} normald t .

Due to existence of a long memory behavior in fractional operator, when α is noninteger, Newton's binomial

((), \begin{array}{c} α \\ j \end{array})

convergence speed to zero with j will be very slow. In accordance with the short memory principle for real implementation, approximation of Equation using only the recent past values of f ( t ) is definable as

D^{α} f ((), t) = \frac{1}{h^{α}} \sum_{j = 0}^{N} {(- 1)}^{j} ((), \begin{array}{c} α \\ j \end{array}) f ((), t - j h),

where N = [ T / h ] specify the approximation addends number …”

Section: The Miso Hammerstein Modelmentioning

confidence: 99%

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

Moghaddam

Mojallali

Teshnehlab

2018

Math Methods in App Sciences

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This paper presents a new multiple-input-single-output nonlinear system identification method based on Hammerstein model, which includes a fractional transfer function and a Modified Radial Basis Function Neural Network (MRBFNN) as linear dynamic part and static nonlinear subsystem, respectively. The size of Radial Basis Function Neural Network (RBFNN) grows with the number of inputs exponentially. As a novel idea, the MRBFNN is proposed, whose adjustable parameters are far fewer than other RBFNNs presented yet. A Modified Genetic Algorithm is used to identify the fractional orders and the centers and widths of MRBFNN and obtain an initial estimation of other unknown parameters. The Recursive Least Square (RLS) method is used to improve the estimation by updating the weighting parameters of MRBFNN and the transfer function coefficients. The convergence analysis of the proposed RLS is provided. Simulation results show the effectiveness and accuracy of the proposed method. KEYWORDS fractional order, genetic algorithm, Hammerstein model, modified radial basis function, nonlinear system identification 6252

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“…) denotes Euler's Gamma function, with the following definition:

normalΓ ((), n) = \int_{0}^{\infty} t^{n - 1} e^{- t} normald t .

Due to existence of a long memory behavior in fractional operator, when α is noninteger, Newton's binomial

((), \begin{array}{c} α \\ j \end{array})

D^{α} f ((), t) = \frac{1}{h^{α}} \sum_{j = 0}^{N} {(- 1)}^{j} ((), \begin{array}{c} α \\ j \end{array}) f ((), t - j h),

where N = [ T / h ] specify the approximation addends number …”

Section: The Miso Hammerstein Modelmentioning

confidence: 99%

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

Moghaddam

Mojallali

Teshnehlab

2018

Math Methods in App Sciences

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“…Based on what discussed in [24], to get the optimal estimation the following objective function have to minimized. (16) Moreover, to ensure that the system has the identifiability property, the …”

Section: The Model Used For Identificationmentioning

confidence: 99%

Fractional order state space canonical model identification using fractional order information filter

Safarinejadian

Asad

2015

2015 the International Symposium on Artificial Intelligence and Signal Processing (AISP)

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In the present paper the identification and estimation problem of a fractional order state space system will be addressed. This paper presents a fractional order information filter and also a hierarchical identification algorithm to identify and estimate parameters and states of a fractional order system. Then, merging this algorithm with fractional order information filter, a novel identification method based on hierarchical identification theory is introduced to reduce the computational complexity. Finally, the applicability and performance of this platform on an exemplary system is examined.

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“…One of the standard methods for the identification of systems with integer order derivatives is to use the leastsquares method [28]. This method was generalized to fractional order systems in [4], [5]. In this method, we need to estimate the fractional derivatives of y and u using a fractional order differentiator [29], [30], [31].…”

Section: A Fractional Order Linear Systemsmentioning

confidence: 99%

“…We can classify these methods into time domain methods and frequency domain methods. Timedomain methods have been introduced for example in [4], [5], where a method based on the discretization of a fractional differential equation using Grunwald definition has been introduced, and the parameters have been estimated using least square approach. In [6], a method based on the approximation of a fractional integrator by a rational model has been proposed.…”

Section: Introductionmentioning

confidence: 99%

Identification of fractional order systems using modulating functions method

Liu

Laleg‐Kirati

Gibaru

et al. 2013

2013 American Control Conference

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Abstract-The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

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Recursive prediction error identification of fractional order models

Cited by 42 publications

References 6 publications

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

A multiple‐input–single‐output fractional‐order Hammerstein model identification based on modified neural network

Fractional order state space canonical model identification using fractional order information filter

Identification of fractional order systems using modulating functions method

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