A novel approach of fractional-order time delay system modeling based on Haar wavelet

Kothari, Kajal; Mehta, Utkal; Vanualailai, Jito

doi:10.1016/j.isatra.2018.07.019

Cited by 45 publications

(27 citation statements)

References 30 publications

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“…Haar wavelet has several applications in diverse areas of research. A portion of the current work utilizing wavelets can be found in the references [2][3][4][5][6][7]. Different researchers utilized wavelets for approximate solutions of IEs [8], boundary value problems [9], PDEs [10], fractional PDEs [11] and delay PDEs [12].…”

Section: To Develop Efficient Technique For the Approximate Solution mentioning

confidence: 99%

A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things

Amin

Nazir

García‐Magariño

2020

Sensors

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Wireless sensor network and industrial internet of things have been a growing area of research which is exploited in various fields such as smart home, smart industries, smart transportation, and so on. There is a need of a mechanism which can easily tackle the problems of nonlinear delay integro-differential equations for large-scale applications of Internet of Things. In this paper, Haar wavelet collocation technique is developed for the solution of nonlinear delay integro-differential equations for wireless sensor network and industrial Internet of Things. The method is applied to nonlinear delay Volterra, delay Fredholm and delay Volterra–Fredholm integro-differential equations which are based on the use of Haar wavelets. Some examples are given to show the computational efficiency of the proposed technique. The approximate solutions are compared with the exact solution. The maximum absolute and mean square roots errors for distant number of collocation points are also calculated. The results show that Haar method is efficient for solving these equations for industrial Internet of Things. The results are compared with existing methods from the literature. The results exhibit that the method is simple, precise and efficient.

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Section: To Develop Efficient Technique For the Approximate Solution mentioning

confidence: 99%

A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things

Amin

Nazir

García‐Magariño

2020

Sensors

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“…Basically, the operational matrix of fractional order integration transforms integral/derivative terms into algebraic matrix multiplications. The operational matrix can be generated using different orthogonal series, for example, block pulse functions [3,4], Legendre wavelet [5], Haar wavelets [6,7], Chebyshev polynomials [8], Taylor series, etc. This method reduces the complexity of identification with higher efficiency.…”

Section: Fractional-order Modelingmentioning

confidence: 99%

“…The system with time delay was approximated using the Haar wavelet technique, presented recently in [7] and other using block pulse functions presented in [3]. The approximated fractional-order models and integer-order models for both and are as shown in Table 3 where depicts time-domain error and represents frequencydomain error.…”

Section: (4) (5)mentioning

confidence: 99%

Fractional-Order System Modeling and its Applications

Kothari¹,

Mehta²,

Prasad³

2019

JESTR

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In order to control or operate any system in a closed-loop, it is important to know its behavior in the form of mathematical models. In the last two decades, a fractional-order model has received more attention in system identification instead of classical integer-order model transfer function. Literature shows recently that some techniques on fractional calculus and fractional-order models have been presenting valuable contributions to real-world processes and achieved better results. Such new developments have impelled research into extensions of the classical identification techniques to advanced fields of science and engineering. This article surveys the recent methods in the field and other related challenges to implement the fractional-order derivatives and miss-matching with conventional science. The comprehensive discussion on available literature would help the readers to grasp the concept of fractional-order modeling and can facilitate future investigations. One can anticipate manifesting recent advances in fractional-order modeling in this paper and unlocking more opportunities for research.

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“…where ( a 1 , a 0 , α ∈ R + ) are estimations of the linear subsystem parameters. Through minimization of an objective function, the linear subsystem parameters can be estimated , and a time-moment weighted integral performance criterion, such as the integral of squared-time-weighted error (ISTE), is suitable for such problems [20]. It is defined as…”

Section: Parameter Identification Of the Fractional Hammerstein Systementioning

confidence: 99%

“…To reduce computational complexity when identifying non-integer orders, the representation of the fractional operator with a generalized operational matrix through orthogonal basis functions, such as a block pulse [17] and the Haar wavelet [18], are more suitable solutions. Although this technique was extended to linear systems with time delay [19,20], its utilization in the nonlinear case has been relatively scarce.…”

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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A novel approach of fractional-order time delay system modeling based on Haar wavelet

Cited by 45 publications

References 30 publications

A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things

A Collocation Method for Numerical Solution of Nonlinear Delay Integro-Differential Equations for Wireless Sensor Network and Internet of Things

Fractional-Order System Modeling and its Applications

Parametric Identification of Nonlinear Fractional Hammerstein Models

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