Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Rajchakit, Grienggrai; Chanthorn, Pharunyou; Kaewmesri, Pramet; Sriraman, Ramalingam; Lim, Chee Peng

doi:10.3390/math8030422

Cited by 90 publications

(37 citation statements)

References 42 publications

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“…Recently, several activation functions have been considered to study the QVNNs. 5,53,58,59 Two different approaches have been well regarded among them. The first approach is that the activation functions are not expressed directly by dividing real and imaginary parts, 59 and the second approach is that the function of activation can be expressed by dividing real and imaginary parts.…”

Section: Model Descriptionmentioning

confidence: 99%

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Aouiti

Jallouli

2021

Intl J Robust & Nonlinear

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This article addresses the problems of fixed-time stabilization for a class of quaternion fuzzy neural networks (QFNNs) with time-varying delay. The QFNNs are developed by dividing our system into four real-valued parts based on the Hamilton rule. Then, based on fixed-time stability theory, some inequality techniques, and selecting the appropriate controllers and Lyapunov function, a novel criterion guaranteeing the fixed-time stabilization and the finite-time stabilization of the addressed system is derived. Finally, three numerical examples are presented to show the effectiveness of our theoretical results. K E Y W O R D S finite-time stabilization, fixed-time stabilization, fuzzy neural networks, quaternion neural networks, time-varying delay

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Section: Model Descriptionmentioning

confidence: 99%

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Aouiti

Jallouli

2021

Intl J Robust & Nonlinear

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“…There are a lot of scientific research papers that applied similar procedures in various areas of science. Most of them are based on new achievements in ANN, for example [2][3][4][5][6], whereas some of them were applied in maritime industry, for example [7][8][9].…”

Section: Literature Reviewmentioning

confidence: 99%

Applying artificial neural networks for modelling ship speed and fuel consumption

Tarełko

Rudzki

2020

Neural Comput & Applic

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This paper deals with modelling ship speed and fuel consumption using artificial neural network (ANN) techniques. These tools allowed us to develop ANN models that can be used for predicting both the fuel consumption and the travel time to the destination for commanded outputs (the ship driveline shaft speed and the propeller pitch) selected by the ship operator. In these cases, due to variable environmental conditions, making decisions regarding setting the proper commanded outputs to is extraordinarily difficult. To support such decisions, we have developed a decision support system. Its main elements are the ANN models enabling ship fuel consumption and speed prediction. To collect data needed for building ANN models, sea trials were conducted. In this paper, the decision support system concept, input and variables of the ship driveline system models, and data acquisition methods are presented. Based on them, we developed appropriate ANN models. Subsequently, we performed a quality assessment of the collected data set, data normalization and division of the data set, selection of an ANN model architecture and assessment of their quality.

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“…23 By using the method of Lyapunov fractional-order derivative, stabilization conditions for considered quaternion-valued memristive neural networks are established. 24 Some scholars give two different methods to obtain criteria of -stability of QVNNs based on linear matrix inequality. 25 There are also some researches on the boundedness and discrete time-delay QVNNs with global exponential periodicity, 26 and analyses on the global dispersion of the time-varying delay QVNNs.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the quaternions can also be decomposed into four different real‐valued parts to research exponential stability of the asynchronous delay QVNNs 23 . By using the method of Lyapunov fractional‐order derivative, stabilization conditions for considered quaternion‐valued memristive neural networks are established 24 . Some scholars give two different methods to obtain criteria of

μ

‐stability of QVNNs based on linear matrix inequality 25 .…”

Section: Introductionmentioning

confidence: 99%

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

Lou

et al. 2020

Intl J Robust & Nonlinear

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In this article, the stability of quaternion-valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, T < ∞ and T = ∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p-norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.

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Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Cited by 90 publications

References 42 publications

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

New feedback control techniques of quaternion fuzzy neural networks with time‐varying delay

Applying artificial neural networks for modelling ship speed and fuel consumption

A unified criterion for global exponential stability of quaternion‐valued neural networks with hybrid impulses

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