Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

Yan, Hongyun; Qiao, Yuanhua; Duan, Lijuan; Zhang, Ling

doi:10.1155/2020/6398208

Cited by 3 publications

(2 citation statements)

References 29 publications

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“…For fractional-order systems, the concept of Mittag-Leffler stability was introduced in [23]. This notion generalizes the exponential stability notion for integer-order systems and has been investigated intensively [23][24][25][26][27][28][29]34,44]. In this section, we establish criteria for the global Mittag-Leffler stability of the error system (8).…”

Section: Global Mittag-leffler Synchronizationmentioning

confidence: 99%

“…Podlubny and his coauthors proposed in [23] the Mittag-Leffler stability notion and the fractional Lyapunov direct approach to extend the use of fractional calculus in nonlinear systems, with the goal of improving both system theory and fractional calculus knowledge. Since then, the stability of Mittag-Leffler, generalized Mittag-Leffler stability, and synchronization have been examined for different classes of fractional-order neural networks [24][25][26][27], including BAM neural network models [28,29].…”

Section: Introductionmentioning

confidence: 99%

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Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

Syed Ali,

Stamov,

Stamova

et al. 2023

Mathematics

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In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results.

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Section: Global Mittag-leffler Synchronizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

Syed Ali,

Stamov,

Stamova

et al. 2023

Mathematics

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Artificial neural networks: a practical review of applications involving fractional calculus

Viera-Martin

Gómez-Aguilar

Solís-Pérez

et al. 2022

Eur. Phys. J. Spec. Top.

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In this work, a bibliographic analysis on artificial neural networks (ANNs) using fractional calculus (FC) theory has been developed to summarize the main features and applications of the ANNs. ANN is a mathematical modeling tool used in several sciences and engineering fields. FC has been mainly applied on ANNs with three different objectives, such as systems stabilization, systems synchronization, and parameters training, using optimization algorithms. FC and some control strategies have been satisfactorily employed to attain the synchronization and stabilization of ANNs. To show this fact, in this manuscript are summarized, the architecture of the systems, the control strategies, and the fractional derivatives used in each research work, also, the achieved goals are presented. Regarding the parameters training using optimization algorithms issue, in this manuscript, the systems types, the fractional derivatives involved, and the optimization algorithm employed to train the ANN parameters are also presented. In most of the works found in the literature where ANNs and FC are involved, the authors focused on controlling the systems using synchronization and stabilization. Furthermore, recent applications of ANNs with FC in several fields such as medicine, cryptographic, image processing, robotic are reviewed in detail in this manuscript. Works with applications, such as chaos analysis, functions approximation, heat transfer process, periodicity, and dissipativity, also were included. Almost to the end of the paper, several future research topics arising on ANNs involved with FC are recommended to the researchers community. From the bibliographic review, we concluded that the Caputo derivative is the most utilized derivative for solving problems with ANNs because its initial values take the same form as the differential equations of integer-order.

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Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities

Zhang

2022

Mathematics

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In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers.

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Global Mittag–Leffler Stabilization of Fractional-Order BAM Neural Networks with Linear State Feedback Controllers

Cited by 3 publications

References 29 publications

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers

Artificial neural networks: a practical review of applications involving fractional calculus

Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities

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