Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter

Wiora, Alicja

doi:10.3390/sym12111898

Cited by 18 publications

(9 citation statements)

References 62 publications

(76 reference statements)

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“…The definition of the integro-differential equation operator is presented in the study [64][65][66][67][68][69][70][71]:…”

Section: Fractional Order Calculusmentioning

confidence: 99%

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Fractional Order Sliding Mode Controller for HBV Epidemic System

Boonyaprapasorn¹,

Kuntanapreeda²,

Ngaimsunthorn³

et al. 2022

MMEP

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The Hepatitis-B (HBV) epidemic's dynamic can be presented as a compartment model. Determining the HBV epidemic control strategy can be considered a nonlinear feedback control problem. The sliding mode controller (SMC) is an effective feedback control method for controlling the dynamical system under disturbances. Recently, the SMC based on fractional order calculus can provide preferable characteristics for a control system such as robustness and convergence rate. In this study, the HBV epidemic system's control policy is proposed using the fractional order sliding mode controller (FOSMC). The control policy with multiple measures including vaccination, isolation, and treatment is formulated to manipulate the susceptible and the infected subpopulations to the desired level. The Lyapunov-based approach is proven for stability analysis. The control policy is applied to the simulation example to verify the feasibility of the proposed FOSMC method. The simulation results are compared with those of the integer order SMC. By the proposed method, the results reveal that the susceptible and infected subpopulations are driven to the desired levels under disturbances with a higher convergence rate compared to that of the integer one. Moreover, the proposed FOSMC method can reduce the chattering occurrence which is the primary drawback of the SMC method.

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“…The definition of the integro-differential equation operator is presented in the study [64][65][66][67][68][69][70][71]:…”

Section: Fractional Order Calculusmentioning

confidence: 99%

“…The order  could be real or complex number. The upper and lower limit of operation are denoted by a and t. Three common definitions of fractional order derivative are presented as follows [64][65][66][67][68][69][70][71]: Riemann Louisville's definition…”

Section: Fractional Order Calculusmentioning

confidence: 99%

Fractional Order Sliding Mode Controller for HBV Epidemic System

Boonyaprapasorn¹,

Kuntanapreeda²,

Ngaimsunthorn³

et al. 2022

MMEP

View full text Add to dashboard Cite

show abstract

“…Theorem 2. Assume that y(t) and y N (t) are the exact and approximate solutions of Equation (4), respectively, such that our estimate solution obtain from (14). Then, we have the following:…”

Section: Lemmamentioning

confidence: 99%

“…However, there are some difficulties in the realization of fractional order systems, due to the fractional derivative and integral terms. To overcome these difficulties and realize fractional operators as well as possible, several integer order approximation methods were proposed by the researchers of [14][15][16][17]. The important feature of problem (1) is the difficulty of finding numerical methods with a low computing cost and enough accuracy, and analytically handling solutions.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule

2021

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This paper introduces an efficient numerical scheme for solving a significant class of fractional differential equations. The major contributions made in this paper apply a direct approach based on a combination of time discretization and the Laplace transform method to transcribe the fractional differential problem under study into a dynamic linear equations system. The resulting problem is then solved by employing the numerical method of the quadrature rule, which is also a well-developed numerical method. The present numerical scheme, which is based on the numerical inversion of Laplace transform and equal-width quadrature rule is robust and efficient. Some numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.

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“…e new approach, based on fractional filters [26], is then implemented on a dynamical model of an exoskeleton and simulation results are presented. Good performances validate the L 1 adaptive fractional controller.…”

Section: Introductionmentioning

confidence: 99%

$L_{1}$ Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems

Maalej

Khlif

Mhiri

et al. 2021

Mathematical Problems in Engineering

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Recently, an adaptive control approach has been proposed. This approach, named L 1 adaptive control, involves the insertion of a low-pass filter at the input of the Model Reference Adaptive Control (MRAC). This controller has been designed to overcome several limitations of classical adaptive controllers such as (i) the initialization of estimated parameters, (ii) the stability problems with high adaptation gains, and (iii) the appropriate parameter excitation. In this paper, a new design of the filter is presented, used for L 1 adaptive control, for which the desired performances are guaranteed (appropriate values of the control during start-up, a high filtering of noises, a reduced time lag, and a reduced energy consumption). Parameters of the new proposed filter have been optimised by genetic algorithms. The proposed L 1 adaptive fractional control is applied to a polyarticulated robotic system. Simulation results show the efficiency of the proposed control approach with respect to the classical L 1 adaptive control in the nominal case and in the presence of a multiplicative noise.

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Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter

Cited by 18 publications

References 62 publications

Fractional Order Sliding Mode Controller for HBV Epidemic System

Fractional Order Sliding Mode Controller for HBV Epidemic System

Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule

$L_{1}$ Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems

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Influence of Methods Approximating Fractional-Order Differentiation on the Output Signal Illustrated by Three Variants of Oustaloup Filter

Cited by 18 publications

References 62 publications

Fractional Order Sliding Mode Controller for HBV Epidemic System

Fractional Order Sliding Mode Controller for HBV Epidemic System

Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule

L 1 Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems

Contact Info

Product

Resources

About

$L_{1}$ Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems