Generalized Lag Synchronization of Neural Networks with Discontinuous Activations and Bounded Perturbations

Wu, Enhua; Yang, Xinsong

doi:10.1007/s00034-014-9962-7

Cited by 16 publications

(5 citation statements)

References 29 publications

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“…Hence, investigating synchronization of discontinuous NNs has attracted considerable attention. Recently, based on Filippov set‐valued map , several results concerning synchronization of NNs with discontinuous activation functions are obtained .…”

Section: Introductionmentioning

confidence: 99%

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Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

Yang

et al. 2018

Asian Journal of Control

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In this paper, finite-time synchronization for a class of complex-valued neural networks with time delays and discontinuous activations is concerned under the framework of Filippov solutions. Both state feedback and adaptive controllers are designed to overcome the difficulties in dealing with the time delay and the uncertainties of Filippov solutions. Based on the concept of Filippov solutions, differential inclusion and structuring suitable Lyapunov-Krasovskii functionals, some sufficient conditions are obtained to guarantee that a controlled response system is synchronized with a driving system in a finite time. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

“…Synchronization in the references mentioned above are asymptotic , that is to say the synchronization can only be realized when time goes to infinity. However, in practical applications, synchronization is always expected to be achieved as fast as possible.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

Yang

et al. 2018

Asian Journal of Control

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“…Therefore, when dealing with dynamical systems possessing high-slope nonlinear elements, differential equations with discontinuous right-hand side is of great importance to the construction of model. Driven by interests, in recent years, a growing number of scholars have devoted themselves to the study of NNs with discontinuous or non-Lipschitz activation functions [41,45,46].…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

Liu

Wan

et al. 2018

NAMC

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In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results.

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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%

“…By designing discontinuous state-feedback controller, exponential synchronization for NNs with discontinuous activations and time-varying delays was developed in Cai et al (2015). Wu and Yang (2015) proposed generalized lag synchronization for a class of NNs with discontinuous activation functions and bounded external disturbances under the framework of Filippov solutions. presented general decay synchronization for a class of delayed chaotic NNs with discontinuous activations.…”

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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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Generalized Lag Synchronization of Neural Networks with Discontinuous Activations and Bounded Perturbations

Cited by 16 publications

References 29 publications

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

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

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