Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Zhang, Jine

doi:10.1155/2017/9323172

Cited by 10 publications

(23 citation statements)

References 34 publications

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“…Compared with an isolated system, coupled systems have wider applications in many fields [23,24,25], such as robots, dynamic image processing, associative memory of video. Therefore, some dynamic characteristics of coupled systems were investigated in recent years [25,26,27,28,29,30,31,32,33,34,35,36]. For example, synchronization of coupled NN systems was researched in [30,31] and [35].…”

Section: Introductionmentioning

confidence: 99%

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Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

et al. 2019

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In this paper, we focus on synchronization issue of coupled multistable memristive neural networks (CMMNNs) with time delay under multiple stable equilibrium states. First, we build delayed CMMNNs consisting of one master subnetwork without controller and N − 1 identical slave subnetworks with controllers, and every subnetwork has n nodes. Moreover, this paper investigates multistability of delayed CMMNNs with continuous nonmonotonic piecewise linear activation function (PLAF) owning 2r + 2 corner points. By using the theorems of differential inclusion and fixed point, sufficient conditions are derived such that master subnetwork of CMMNNs can acquire (r + 2) n exponentially stable equilibrium points, stable periodic orbits or hybrid stable equilibrium states. Then, this paper proposes hybrid multisynchronization of delayed CMMNNs related with various external inputs under multiple stable equilibrium states for the first time. There exist (r + 2) n hybrid multisynchronization manifolds in CMMNNs with different initial conditions and external inputs. Finally, two numerical simulations are given to illustrate the effectiveness of the obtained results.

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Section: Introductionmentioning

confidence: 99%

“…In [32,33,34], multistability and multisynchronization of coupled multistable NN systems were investigated. However, there is no relevant work on studying dynamic characteristics of coupled multistable MNN (CMMNN) systems.…”

Section: Introductionmentioning

confidence: 99%

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

et al. 2019

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“…It is a complex nonlinear relationship between rugosity M ij,1 , standard deviation M ij,2 , skewness M ij,3 , kurtosis M ij, 4 and feed speed Vc, peripheral speed Vw, axial displacement f a , radial displacement f r in (18). The nonlinear relationship between them is described using deep neural networks.…”

Section: Grinding Robot Prediction Algorithm Of Controllermentioning

confidence: 99%

“…A stability criterion of impulsive stochastic reactiondiffusion cellular neural network framework was derived via fixed-point theory [17]. The subnetwork of a class of coupled fractional-order neural networks consisting of N identical subnetworks have r + 1 n locally Mittag-Leffler stable equilibria [18]. Our work was implemented based on these frameworks.…”

Section: Introductionmentioning

confidence: 99%

Eigen Solution of Neural Networks and Its Application in Prediction and Analysis of Controller Parameters of Grinding Robot in Complex Environments

Tang

et al. 2019

Complexity

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The robot dynamic model is often rarely known due to various uncertainties such as parametric uncertainties or modeling errors existing in complex environments. It is a key problem to find the relationship between the changes of neural network structure and the changes of input and output environments and their mutual influences. Firstly, this paper defined the conceptions of neural network solution, neural network eigen solution, neural network complete solution, and neural network partial solution and the conceptions of input environments, output environments, and macrostructure of neural networks. Secondly, an eigen solution theory of general neural networks was proposed and proven including consistent approximation theorem, eigen solution existence theorem, consistency theorem of complete solution, the partial solution, and none solution theorem of neural networks. Lastly, to verify the eigen solution theory of neural networks, the proposed theory was applied to a novel prediction and analysis model of controller parameters of grinding robot in complex environments with deep neural networks and then build prediction model with deep learning neural networks for controller parameters of grinding robot. The morphological subfeature graph with multimoment was constructed to describe the block surface morphology using rugosity, standard deviation, skewness, and kurtosis. The results of theoretical analysis and experimental test show that the output traits have an optional effect with joint action. When the input features functioning in prediction increase, higher predicted accuracy can be obtained. And when the output traits involving in prediction increase, more output traits can be predicted. The proposed prediction and analysis model with deep neural networks can be used to find and predict the inherent laws of the data. Compared with the traditional prediction model, the proposed model can predict output features simultaneously and is more stable.

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“…Recently, in Yıldız [12] the dynamics of a waterborne pathogen fractional model under the influence of environmental pollution has been studied and the solutions of a generalized fractional kinetic equations are obtained [13] using the generalized fractional integrations of the generalized Mittag-Leffler type function. Finally, we highlight that different fractional systems have also been considered in the framework of control theory [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Basic Control Theory for Linear Fractional Differential Equations With Constant Coefficients

Buedo‐Fernández

Nieto

2020

Front. Phys.

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In this paper we present an analogous result of the famous Kalman controllability criterion for first order linear ordinary differential equations with constant coefficients that applies to the case of linear differential equations of fractional order with constant coefficients. We use the fractional Gramian matrix, the range space and the Kalman matrix as main tools to derive a sufficient and necessary condition for the controllability of the fractional system. Moreover, we provide some simple examples, including a linear fractional harmonic oscillator, to illustrate our results. Finally, several open problems arising from this topic are suggested, including another simple linear system of incommensurate fractional orders.

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Multisynchronization for Coupled Multistable Fractional-Order Neural Networks via Impulsive Control

Cited by 10 publications

References 34 publications

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Hybrid multisynchronization of coupled multistable memristive neural networks with time delays

Eigen Solution of Neural Networks and Its Application in Prediction and Analysis of Controller Parameters of Grinding Robot in Complex Environments

Basic Control Theory for Linear Fractional Differential Equations With Constant Coefficients

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