Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

Cui, Baotong; Lou, Xuyang

doi:10.1016/j.chaos.2007.01.100

Cited by 64 publications

(33 citation statements)

References 20 publications

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“…Then, the derivative of V(t) with respect to time t along the systems (3), (15) is given as When kek 6 ¼ 0 and t 2 ½lT ; lT 1dT Þ; by (13), (14), (17), and Assumption 1, by (9) and (10) When kek50 or t 2 ½lT 1dT ; lT 1T Þ; by (17), (13), (14), and Assumption 1, Obviously, by the conditions (i) and (ii) of Theorem 2, it yields _ V ðtÞ 0:…”

Section: Theoremmentioning

confidence: 99%

“…[6][7][8]. Accordingly, various of controllers are proposed to solve some problems of synchronization between neural networks, such as adaptive control [9][10][11][12], nonlinear feedback control [13,14], sliding mode control [15,16], descriptor model transformation method [17], etc.…”

Section: Introductionmentioning

confidence: 99%

“…So, many existing works of time delays have been investigated [18][19][20][21]. It has also been Correspondence to: Taiyan Jing, E-mail: taiyan825@163.com discovered that time delay coupling has great influence on the behavior of dynamical systems [22,23].…”

Section: Introductionmentioning

confidence: 99%

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Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

Jing

Chen

2015

Complexity

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The problem of finite-time lag synchronization of delayed neural networks via periodically intermittent control is studied. In two sections, based on the same finite-time stability theory and using the same sliding mode control, by designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws, we achieve the finite-time lag synchronization between two time delayed networks. In addition, we ensure that the trajectory of the error system converges to a chosen sliding surface within finite time and keeps it on forever. Finally, two examples are presented to verify the effectiveness of the analytical results obtained here.

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Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

Jing

Chen

2015

Complexity

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“…Many important synchronization control methods have also been developed for CDNs, for instance, feedback control [10,11], intermittent control [4,5], sampled-data control [30], nonlinear feedback control [9,32], pinning control [14,29,33,43], adaptive control [25,31,40,45], pinning adaptive control [19,25,31,39], and other control methods. When controlling a real plant, it is always desirable to design a control system not only asymptotical stability but also guaranteed adequate level of performance.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays

Weera¹,

Botmart²,

Niamsup³

et al. 2018

J. Nonlinear Sci. Appl.

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The problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works.

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“…MFCS design is the method developed based on the idea proposed by Wu, Wang and Okubo [20,21,24]. As is well known, time delays are inherent features of many physical processes, e. g., Chaos system [4,16], engine system [6] and electrical heater [5] and, biological system [8], environmental system [9], network system [22,25], etc. Many of these processes are also significantly nonlinear, which motivates the research into the control of nonlinear systems with time delays [2,6].…”

Section: Introductionmentioning

confidence: 99%

Model following control system with time delays

Wang¹,

Wu²,

Zhang³

et al. 2016

Kybernetika

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Synchronization of chaotic recurrent neural networks with time-varying delays using nonlinear feedback control

Cited by 64 publications

References 20 publications

Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays

Model following control system with time delays

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