Reduced-Order Model Approximation of Fractional-Order Systems Using Differential Evolution Algorithm

Bourouba, Bachir; Ladaci, Samir; Chaabi, Abdelhafid

doi:10.1007/s40313-017-0356-5

Cited by 26 publications

(10 citation statements)

References 34 publications

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“…Among all these methods, the following are the most common power series expansion (PSE) techniques based on Taylor series, Maclaurin series, etc. [40] , [21] , [6] , continued fractional expansion based methods [43] , impulse response based method [29] , time moments based approaches [12] , Carlson method based approaches [7] , optimisation based methods [5] , frequency distribution mode approach [16] , [11] , [19] , [24] , [8] , [45] . …”

Section: Prior Art On the Approximation Of Fractional Order Integratomentioning

confidence: 99%

Beyond the particular case of circuits with geometrically distributed components for approximation of fractional order models: Application to a new class of model for power law type long memory behaviour modelling

Sabatier

2020

Journal of Advanced Research

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Section: Prior Art On the Approximation Of Fractional Order Integratomentioning

confidence: 99%

Beyond the particular case of circuits with geometrically distributed components for approximation of fractional order models: Application to a new class of model for power law type long memory behaviour modelling

Sabatier

2020

Journal of Advanced Research

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“…where a denotes lower limits and t are the upper limits respectively of the operator, and a∈R is the order of integration or differentiation [9,15,16].…”

Section: Fractional-order Definition and Preliminariesmentioning

confidence: 99%

A Novel Non-integer Indirect Adaptive Control for Non-integer Order Systems with Non-prior Knowledge

Bourouba

Ladaci

2020

Eng. Technol. Appl. Sci. Res.

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In this study, a new non-integer indirect adaptive control method with reference model is suggested for the class of non-integer order systems. The objective of model reference control is to include the output of the given reference fractional model in tracking the output of a controlled plant by using the concept of on-line goal adaptation. The stability of the closed-loop system is analyzed via the Lyapunov method. Finally, Matlab simulation results are presented to illustrate the effectiveness of the proposed method of indirect fractional model reference adaptive control.

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“…There exists several approximation approaches; some are temporal, while others are in frequency domain. In the literature, one of the current used approaches in frequency domain is the one of Charef [27,28]. In temporal domain, there is a lot of work about the numerical solution of the fractional differentials equations.…”

Section: Implementation Of Fractional Operatormentioning

confidence: 99%

Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos

Bourouba

Ladaci

2018

Algorithms

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In this paper, a new adaptive fuzzy sliding mode control (AFSMC) design strategy is proposed for the control of a special class of three-dimensional fractional order chaotic systems with uncertainties and external disturbance. The design methodology is developed in two stages: first, an adaptive sliding mode control law is proposed for the class of fractional order chaotic systems without uncertainties, and then a fuzzy logic system is used to estimate the control compensation effort to be added in the case of uncertainties on the system's model. Based on the Lyapunov theory, the stability analysis of both control laws is provided with elimination of the chattering action in the control signal. The developed control scheme is simple to implement and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense if all the involved signals are uniformly bounded. In the present work, simulation studies on fractional-order Chen chaotic systems are carried out to show the efficiency of the proposed fractional adaptive controllers.

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Reduced-Order Model Approximation of Fractional-Order Systems Using Differential Evolution Algorithm

Cited by 26 publications

References 34 publications

Beyond the particular case of circuits with geometrically distributed components for approximation of fractional order models: Application to a new class of model for power law type long memory behaviour modelling

Beyond the particular case of circuits with geometrically distributed components for approximation of fractional order models: Application to a new class of model for power law type long memory behaviour modelling

A Novel Non-integer Indirect Adaptive Control for Non-integer Order Systems with Non-prior Knowledge

Robust Fuzzy Adaptive Sliding Mode Stabilization for Fractional-Order Chaos

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