Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

Liu, Peng; Kong, Minxue; Zeng, Zhigang

doi:10.1109/tcyb.2020.3027755

Cited by 54 publications

(17 citation statements)

References 53 publications

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“…Proof. Noting that by using Assumption 3 and inequality (9), when ‖E(k)‖ > 𝜀, inequality (15) can be written as…”

Section: Designing the Adaptive Controllermentioning

confidence: 99%

“…2 It is known to not all networks can synchronize naturally, and thus the appropriate control schemes are needed to promote network synchronization. 3,4 In recent years, thanks to the great efforts of researchers, a lot of results on synchronization control schemes are proposed for CDNs, such as the complete synchronization, 5,6 generalized synchronization, 7,8 projective synchronization, [9][10][11] cluster synchronization, [12][13][14][15] global synchronization [16][17][18] and so forth.…”

Section: Introductionmentioning

confidence: 99%

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Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

Wang

2022

Adaptive Control & Signal

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This article investigates the outer synchronization for the two discrete-time complex dynamic networks. First, the more universal mathematical models of the networks with unknown coupling and interaction are proposed. Then, based on the available state of networks and the estimation of summarized unknown parameters shown in the models, the adaptive state feedback controller is synthesized to make the outer synchronization error of two networks converge asymptotically to an arbitrarily small neighborhood at the origin. Finally, the results of simulation show the validity and advantages of the controller.

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“…Proof. Noting that by using Assumption 3 and inequality (9), when ‖E(k)‖ > 𝜀, inequality (15) can be written as…”

Section: Designing the Adaptive Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

Wang

2022

Adaptive Control & Signal

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“…If we consider α = 1 in system (1), then the FONNS system with sampled-data control will degenerate to integer order. Accordingly, the asymptotic stability and stability results are still valid for integer order neural network models in [10], [12] and [13].…”

Section: T)p Kx(t − H(t))mentioning

confidence: 99%

Order-dependent sampling control of uncertain fractional-order neural networks system

Zhang

Zhang³

et al. 2022

Preprint

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In this paper, we address the asymptotic stability problem for the fractional-order neural networks system with uncertainty based on sampled-data control. First, considering the influence of uncertainty and fractional-order on the system, a new sampled-data control scheme with variable sampling period is designed. According to the input delay approach, the dynamics of the considered fractional-order system is modeled by a delay system. The main purpose of the problem addressed is to design a sampled-data controller, such that the closed-loop fractional-order system can guarantee the asymptotic stability. Then, the fractional-order Razumishin theorem and linear matrix inequalities (LMIs) are used to derive the stable conditions. The new delay-dependent and order-dependent stability conditions are presented in the form of LMIs. Furthermore, the sampling controller can be obtained to ensure the stability and stabilization of fractional-order system. Finally, a numerical example is given to demonstrate the effectiveness and advantages of the proposed method.

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“…On the other hand, fractional‐order CNNs also increase the degree of freedom through the order of fractional‐order derivatives, which greatly enriches the dynamic behavior 25 . Hence, it becomes a very hot research issue for the dynamic analysis of fractional‐order CNNs, and several significant results for fractional‐order CNNs have been presented 26 . Zhang et al 27 concerned about the exponential stability for fractional‐order CNNs via employing the Mittag–Leffler function and stochastic matrices.…”

Section: Introductionmentioning

confidence: 99%

“…25 Hence, it becomes a very hot research issue for the dynamic analysis of fractional-order CNNs, and several significant results for fractional-order CNNs have been presented. 26 Zhang et al 27 concerned about the exponential stability for fractional-order CNNs via employing the Mittag-Leffler function and stochastic matrices. In the literature, 28 based on the proposed edge-based fractional-order adaptive strategies, several synchronization criteria were acquired by using Barbalat's lemma and fractional-order inequalities.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time synchronization of multi‐weighted fractional‐order coupled neural networks with fixed and adaptive couplings

Tong

Chen

et al. 2022

Adaptive Control & Signal

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This article concentrates on the finite-time synchronization (FTS) for multi-weighted fractional-order coupled neural networks (MFCNNs) with fixed and adaptive couplings. A new dynamic model, which involves coupled neural networks with fractional order and multi-weighted couplings, is proposed. Furthermore, an adaptive law to adjust the coupling weights is devised to ensure the FTS of such a complex model. First, by using fractional-order calculus properties and inequality techniques, a finite-time fractional differential inequality is presented, which considerably extends the prior result. Second, by the Lyapunov stability theory and the fractional-order inequality, several sufficient conditions are acquired to make sure the FTS for MFCNNs. Moreover, the influence of the system's order on the FTS is also uncovered. Finally, a numerical simulation example and a practical simulation example are provided to demonstrate the validity of the obtained criteria.

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Projective Synchronization Analysis of Fractional-Order Neural Networks With Mixed Time Delays

Cited by 54 publications

References 53 publications

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

Outer synchronization for a class of discrete‐time complex dynamic networks with unknown bounded interaction

Order-dependent sampling control of uncertain fractional-order neural networks system

Finite‐time synchronization of multi‐weighted fractional‐order coupled neural networks with fixed and adaptive couplings

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