Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays

Hymavathi, M.; Muhiuddin, G.; Ali, M. Syed; Al-Amri, Jehad F.; Gunasekaran, Nallappan; Vadivel, R.

doi:10.3390/fractalfract6030140

Cited by 10 publications

(4 citation statements)

References 37 publications

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“…e dynamics of complex networks have been widely studied on the basis of complex network models, with a focus on the interaction between the complexity of the overall topology and the local dynamical characteristics of the connected nodes. Hence, fractional-order complex networks can better model and reveals some remarkable results have been obtained [11][12][13][14]. e behaviour of the network nodes is similar throughout the existing literature on complex dynamical networks that takes drive and response systems under consideration.…”

Section: Introductionsupporting

confidence: 56%

Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Alsulami

Ali

Hymavathi

et al. 2022

Mathematical Problems in Engineering

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In this article, global asymptotic stability analysis, and mixed ℋ ∞ and passive control for a class of control fractional-order systems is investigated. Based on the fractional-order Lyapunov stability theorem and some properties of fractional calculus, we propose sufficient conditions to ensure the mixed ℋ ∞ and passivity performance. More relaxed conditions by employing the new type of augmented matrices by using Kronecker product terms can be handled, which can be introduced. The derived criteria are expressed in terms of linear matrix inequalities that which can be checked numerically using toolbox MATLAB. Finally, two numerical examples are provided to demonstrate the correctness of the proposed results.

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Section: Introductionsupporting

confidence: 56%

Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Alsulami

Ali

Hymavathi

et al. 2022

Mathematical Problems in Engineering

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“…Further research should concentrate on improving the learning method of Artificial Neural networks with newer algorithms. For example, in papers [48,49] based on the Lyapunov-Krasovskii functional, reciprocally convex technique, Jensen's inequality reduced the communication load in the network. An event-triggering scheme filtering has been proposed for delayed neural networks with sampled data and some suitable sufficient conditions of the considered neural networks were achieved.…”

Section: Discussionmentioning

confidence: 99%

Artificial Neural Network Structure Optimisation in the Pareto Approach on the Example of Stress Prediction in the Disk-Drum Structure of an Axial Compressor

Kozakiewicz

Kieszek

2022

Materials

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The article presents the process of selecting and optimising artificial neural networks based on the example of determining the stress distribution in a disk-drum structure compressor stage of an aircraft turbine engine. The presented algorithm allows the determination of von Mises stress values which can be part of the penalty function for further mass optimization of the structure. A method of a parametric model description of a compressor stage is presented in order to prepare a reduced stress distribution for training artificial neural networks. A comparative analysis of selected neural network training algorithms combined with the optimisation of their structure is presented. A genetic algorithm was used to determine the optimal number of hidden layers and neurons in a layer. The objective function was to minimise the absolute value of the relative error and standard deviation of stresses determined by FEM and artificial neural networks. The results are presented in the form of the Pareto front due to the stochastic optimisation process.

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“…To the best of our knowledge, this type of model has not been studied before in the existing literature. There exist, however, papers discussing fractional-order CVNNs (FOCVNNs), for example, [32,37,[46][47][48][49], and also papers dealing with different dynamic properties of fractional-order QVNNs (FOQVNNs), for example, [29,35,[42][43][44]50]. As such, the current research presents a model that generalizes the models proposed in these papers.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

Popa

2023

Fractal Fract

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Very recently, a different generalization of real-valued neural networks (RVNNs) to multidimensional domains beside the complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and Clifford-valued neural networks (ClVNNs) has appeared, namely octonion-valued neural networks (OVNNs), which are not a subset of ClVNNs. They are defined on the octonion algebra, which is an 8D algebra over the reals, and is also the only other normed division algebra that can be defined over the reals beside the complex and quaternion algebras. On the other hand, fractional-order neural networks (FONNs) have also been very intensively researched in the recent past. Thus, the present work combines FONNs and OVNNs and puts forward a fractional-order octonion-valued neural network (FOOVNN) with neutral-type, time-varying, and distributed delays, a very general model not yet discussed in the literature, to our awareness. Sufficient criteria expressed as linear matrix inequalities (LMIs) and algebraic inequalities are deduced, which ensure the asymptotic and Mittag–Leffler synchronization properties of the proposed model by decomposing the OVNN system of equations into a real-valued one, in order to avoid the non-associativity problem of the octonion algebra. To accomplish synchronization, we use two different state feedback controllers, two different types of Lyapunov-like functionals in conjunction with two Halanay-type lemmas for FONNs, the free-weighting matrix method, a classical lemma, and Young’s inequality. The four theorems presented in the paper are each illustrated by a numerical example.

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Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays

Cited by 10 publications

References 37 publications

Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Artificial Neural Network Structure Optimisation in the Pareto Approach on the Example of Stress Prediction in the Disk-Drum Structure of an Axial Compressor

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

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Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays

Cited by 10 publications

References 37 publications

Mixed ℋ ∞ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Mixed ℋ ∞ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Artificial Neural Network Structure Optimisation in the Pareto Approach on the Example of Stress Prediction in the Disk-Drum Structure of an Axial Compressor

Asymptotic and Mittag–Leffler Synchronization of Fractional-Order Octonion-Valued Neural Networks with Neutral-Type and Mixed Delays

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Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling

Mixed $ℋ_{\infty}$ and Passivity Analysis of Delayed Fractional-Order Complex Dynamical Networks with Hybrid Coupling