Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems

Soukkou, Ammar; Boukabou, Abdelkrim; Leulmi, Salah

doi:10.1007/s11071-016-2823-0

Cited by 22 publications

(8 citation statements)

References 47 publications

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“…There are several ways to define the fractional calculus, including the Riemann-Liouville (R-L) definition [50,51], the Caputo definition [52], and the Grünwald-Letnikov (G-L) definition [53]. Among them, the R-L definition and the Caputo definition are the most commonly used.…”

Section: The Fractional Calculus and The Mittag-leffler Stability Thementioning

confidence: 99%

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

Liu

Zhang

et al. 2019

Entropy

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Compared with fractional-order chaotic systems with a large number of dimensions, three-dimensional or integer-order chaotic systems exhibit low complexity. In this paper, two novel four-dimensional, continuous, fractional-order, autonomous, and dissipative chaotic system models with higher complexity are revised. Numerical simulation of the two systems was used to verify that the two new fractional-order chaotic systems exhibit very rich dynamic behavior. Moreover, the synchronization method for fractional-order chaotic systems is also an issue that demands attention. In order to apply the Lyapunov stability theory, it is often necessary to design complicated functions to achieve the synchronization of fractional-order systems. Based on the fractional Mittag–Leffler stability theory, an adaptive, large-scale, and asymptotic synchronization control method is studied in this paper. The proposed scheme realizes the synchronization of two different fractional-order chaotic systems under the conditions of determined parameters and uncertain parameters. The synchronization theory and its proof are given in this paper. Finally, the model simulation results prove that the designed adaptive controller has good reliability, which contributes to the theoretical research into, and practical engineering applications of, chaos.

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Section: The Fractional Calculus and The Mittag-leffler Stability Thementioning

confidence: 99%

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

Liu

Zhang

et al. 2019

Entropy

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“…Synchronization has received a lot of interest in applications in different fields [ 1 , 2 , 3 , 4 ], and in recent years, chaotic synchronization has received attention in the implementation of private and secure communication systems [ 1 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ]. Confidential information is encrypted into a transmission using a chaotic signal by direct modulation, masking, or other techniques [ 7 , 11 ].…”

Section: Introductionmentioning

confidence: 99%

Network Synchronization of MACM Circuits and Its Application to Secure Communications

Méndez-Ramírez

Arellano-Delgado

Murillo-Escobar

2023

Entropy

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In recent years, chaotic synchronization has received a lot of interest in applications in different fields, including in the design of private and secure communication systems. The purpose of this paper was to achieve the synchronization of the Méndez–Arellano–Cruz–Martínez (MACM) 3D chaotic system coupled in star topology. The MACM electronic circuit is used as chaotic nodes in the communication channels to achieve synchronization in the proposed star network; the corresponding electrical hardware in the slave stages receives the coupling signal from the master node. In addition, a novel application to the digital image encryption process is proposed using the coupled-star-network; and the switching parameter technique is finally used to transmit an image as an encrypted message from the master node to the slave coupled nodes. Finally, the cryptosystem is submitted to statistical tests in order to show the effectiveness in multi-user secure image applications.

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“…In recent decades, fractional-order calculus, as an extension of the well-known integer-order calculus, has been given considerable attention by scholars in the fields of mathematics and engineering (Tlelo-Cuautle et al, 2020). Motivated by the beneficial properties of fractional calculus and its ability to precisely model systems (Soukkou et al, 2018), many research efforts have been concerned with fractional-order dynamical systems, primarily focusing on several important problems, among others, the design of an appropriate control law, the discretization process of fractional-order operators, closed-loop stability analysis, and system modeling (Soukkou et al, 2016). Besides, a descent controller must satisfy both high performances and cost-effectiveness, which made the research area relatively difficult especially when considering chaotic behavior of fractional-order dynamical systems (Soukkou et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Fuzzy L1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

Boulham

Boubakir

Labiod

2023

Transactions of the Institute of Measurement and Control

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This research work proposes a fuzzy fractional-order [Formula: see text] adaptive controller to deal with projective chaos synchronization problems for a general class of uncertain fractional-order chaotic systems subject to unknown input nonlinearities (dead-zone and sector nonlinearities). The suggested control architecture includes a fractional-order sliding surface, a fuzzy system, and an [Formula: see text] adaptive controller. The latter consists of a predictor, a control law, and its adaptive mechanism. The fuzzy system takes the role of an online estimator for system nonlinear uncertain functions which helps in the handling of the input nonlinearities. A designed low-pass filter is placed within the input channel of the [Formula: see text] adaptive controller to ensure that the control loop is decoupled from the estimation loop, which preserves response robustness along with improving transient performances. Finally, the closed-loop stability is rigorously proved, and the acquired results are demonstrated by two simulation examples as well as a comparative study.

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Prediction-based feedback control and synchronization algorithm of fractional-order chaotic systems

Cited by 22 publications

References 47 publications

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order Mittag–Leffler Stability

Network Synchronization of MACM Circuits and Its Application to Secure Communications

Fuzzy L1 adaptive controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

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