Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays

Peng, Xiao; Wu, Huaiqin; Song, Kaidi; Shi, Jiaxin

doi:10.1016/j.neunet.2017.06.011

Cited by 80 publications

(19 citation statements)

References 46 publications

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“…It is well known that the existence of time delay in a network can make system instable and degrade its performance. In recent decades, considerable attention has been devoted to the time-delay systems due to their extensive applications in practical systems including circuit theory, neural network [7][8][9][10] and complex dynamical networks system [11][12][13][14][15][16] etc. Thus, synchronization for complex dynamical networks with time delays in the dynamical nodes and coupling has become a key and significant topic.…”

Section: Introductionmentioning

confidence: 99%

Sliding-mode H ∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Liu

Chen

2019

Adv Differ Equ

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This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov-Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the H ∞ performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results.

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Section: Introductionmentioning

confidence: 99%

Sliding-mode H ∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Liu

Chen

2019

Adv Differ Equ

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“…Most research on the synchronization of delayed neural networks has been restricted to the case of discrete delays (see, for example, [10]) Since a neural network usually has a spatial nature due to the presence of an amount of parallel pathways of a variety of axis sizes and lengths, it is desirable to model them by introducing distributed delays. Note in [11] that both time-varying delays and distributed time delays are taken into account in studying fractional neural networks with impulses and constant strengths between two units.…”

Section: Introductionmentioning

confidence: 99%

“…Note in [11] that both time-varying delays and distributed time delays are taken into account in studying fractional neural networks with impulses and constant strengths between two units. In all models of neural networks, one considers the case of constant rate with which the i-th neuron resets its potential to the resting state in isolation, and the constant synaptic connection strength of the i-th neuron to the j-th neuron (see, for example, [10]). In our paper, we consider the general case of time varying coefficients in the model that allows more appropriate modeling of the connections between the neurons.…”

Section: Introductionmentioning

confidence: 99%

Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

Agarwal

Hristova²,

O’Regan

2018

Symmetry

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The synchronization problem for impulsive fractional-order neural networks with both time-varying bounded and distributed delays is studied. We study the case when the neural networks and the fractional derivatives of all neurons depend significantly on the moments of impulses and we consider both the cases of state coupling controllers and output coupling controllers. The fractional generalization of the Razumikhin method and Lyapunov functions is applied. Initially, a brief overview of the basic fractional derivatives of Lyapunov functions used in the literature is given. Some sufficient conditions are derived to realize the global Mittag–Leffler synchronization of impulsive fractional-order neural networks. Our results are illustrated with examples.

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“…Since being proposed firstly by Pecora and Carroll in 1990 in Pecora and Carroll (1990), chaotic synchronization has emerged as an important research topic in recent years. Many efforts have been paid for studying the synchronization control problems with regard to NNs with discontinuous(or non-Lipschitz) neuron activations in Liu et al (2010Liu et al ( , 2011, Liu and Wu (2019), Cai et al (2015), Wu and Yang (2015), and Peng et al (2017. Liu et al (2010) considered the complete periodic synchronization of delayed NNs with discontinuous activations.…”

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confidence: 99%

“…Non-fragile chaotic synchronization for discontinuous NNs with time delays and random feedback gain uncertainties was discussed in . Peng et al (2017) addressed global finitetime synchronization for fractional-order neural networks with discontinuous activations and time delays.…”

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confidence: 99%

Event-triggered stochastic synchronization in finite time for delayed semi-Markovian jump neural networks with discontinuous activations

Liu

Zhao

2020

Comp. Appl. Math.

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In this paper, the global stochastic synchronization in finite time is discussed for discontinuous semi-Markovian switching neural networks with mixed time-varying delays under stochastic disturbance based on event-triggered non-fragile control scheme. By applying the novel hybrid controller, which is composed of the event-triggered controller, the non-fragile controller and the switching state-feedback controller, the global stochastic synchronization goals in finite time are achieved. Under Filippov differential inclusion framework, based on non-smooth analysis theory, general free-weighting matrix method, Lyapunov-Krasovskii functional approach and inequality analysis technique, the global stochastic synchronization conditions in finite time are addressed in terms of linear matrix inequalities. Moreover, the expressions about the upper bound of stochastic settling time are explicitly developed. Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results. Keywords Discontinuous neural networks • Semi-Markovian switching • Event-triggered non-fragile control scheme • Stochastic synchronization in finite time • Mixed time-varying delays • Noise disturbance Mathematics Subject Classification 93D09 1 Introduction In the past few decades, dynamical neural networks (NNs) have been found because of extensive applications in optimization, image and signal processing, parallel computation, automatic control, associative memories and so on; see Yang and Cao (2008), Liberzon (2003) and Gupta et al. (2003). Such applications bring the considerable attention from a Communicated by Marcos Eduardo Valle.

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Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays

Cited by 80 publications

References 46 publications

Sliding-mode H ∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Sliding-mode H ∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Global Mittag—Leffler Synchronization for Neural Networks Modeled by Impulsive Caputo Fractional Differential Equations with Distributed Delays

Event-triggered stochastic synchronization in finite time for delayed semi-Markovian jump neural networks with discontinuous activations

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