Application of variable-order fractional calculus in neural networks: where do we stand?

Alotaibi, Ahmed; Jahanshahi, Hadi; Castillo, Oscar

doi:10.1140/epjs/s11734-022-00625-3

Cited by 13 publications

(7 citation statements)

References 29 publications

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“…In recently years, the dynamical behavior of fractional-order neural networks (FONN) was widely studied in [22][23][24][25][26][27][28][29][30], especially fractional-order memristive neural networks (FOMNNs) [31][32][33][34][35][36][37][38][39][40][41]. Chen et al investigated Mittag-Leffler synchronization of a FOMNN by using an M-matrix method and set-valued theory in [31].…”

Section: Introductionmentioning

confidence: 99%

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

2022

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This article mainly concentrates on the synchronization problem for a more general kind of the master–slave memristor-based neural networks with fractional derivative. By applying a continuous-frequency-distributed equivalent model tool, some new outcomes and sufficient conditions on the robust synchronization of the master–slave neural networks with uncertainty are proposed via linear matrix inequality (LMI). Finally, two memristive neural networks model with fractional derivatives are presented to validate the efficiency of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

2022

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“…One challenge with machine learning methods, such as the kriging algorithm, is their limited performance in beyond-the-data-range scenarios (Yousefpour et al, 2022). However, our proposed approach mitigates this through a correction term.…”

Section: Comparison With Other Techniquesmentioning

confidence: 99%

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

Alotaibi,

Alsubaie

2024

Journal of Disability Research

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Model predictive control (MPC) has emerged as a predominant method in the realm of control systems; yet, it faces distinct challenges. First, MPC often hinges on the availability of a precise and accurate system model, where even minor deviations can drastically affect the control performance. Second, it entails a high computational load due to the need to solve complex optimization problems in real time. This study introduces an innovative method that harnesses the probabilistic nature of Gaussian processes (GPs), offering a solution that is robust, adaptive, and computationally efficient for optimal control. Our methodology commences with the collection of data to learn optimal control policies. We then proceed with offline training of GPs on these data, which enables these processes to accurately grasp system dynamics, establish input–output relationships, and, crucially, identify uncertainties, thereby informing the MPC framework. Utilizing the mean and uncertainty estimates derived from GPs, we have crafted a controller that is capable of adapting to system deviations and maintaining consistent performance, even in the face of unforeseen disturbances or model inaccuracies. The convergence of the closed-loop system is assured through the application of the Lyapunov stability theorem. In our numerical experiments, the exemplary performance of our approach is demonstrated, notably in its capacity to adeptly handle the complexities of dynamic systems, even with limited training data, underlining a significant leap forward in MPC strategies.

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“…The proposed process for weight evolution of the neural network is described by the following adaptation law equation: . Ŵi = −γ i s it φ i (12) in which γ i denotes a positive design parameter.…”

Section: Super-twisting Controllermentioning

confidence: 99%

“…Recently, some studies have shown that variable-order fractional (VOF) can capture the dynamic of some systems more accurately [12]. The applications of VOF neural networks are vast and promising.…”

Section: Introductionmentioning

confidence: 99%

A Model-Free Finite-Time Control Technique for Synchronization of Variable-Order Fractional Hopfield-like Neural Network

et al. 2023

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Although the literature presents promising techniques for the control of integer-order systems, control and synchronizing fractional systems still need further improvement to ensure their robustness and convergence time. This study aims to address this issue by proposing a model-free and finite-time super-twisting control technique for a variable-order fractional Hopfield-like neural network. The proposed controller is enhanced with an intelligent observer to account for disturbances and uncertainties in the chaotic model of the Hopfield-like neural network. The controller is able to regulate the system even when its complex variable-order fractional dynamic is completely unknown. Moreover, the proposed technique guarantees finite-time convergence of the closed-loop system. First, the dynamics of the variable-order fractional Hopfield-like neural network are examined. Then, the control design is described and its finite-time stability is proven. The controller is then applied to the variable-order fractional system and tested under two different scenarios to evaluate its performance. The results of the simulations demonstrate the excellent performance of the proposed method in both scenarios.

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Application of variable-order fractional calculus in neural networks: where do we stand?

Cited by 13 publications

References 29 publications

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality

Kriging-based Model Predictive Control for Lower-limb Rehabilitation Robots

A Model-Free Finite-Time Control Technique for Synchronization of Variable-Order Fractional Hopfield-like Neural Network

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