Synchronization of coupled reaction–diffusion neural networks via intermittent control and saturated impulses

The impulsive synchronization of coupled neural networks with input saturation and the term of reaction–diffusion via a hybrid control strategy is investigated. In this paper, a hybrid controller is proposed, including impulsive controller with input saturation and intermittent controller. This type of hybrid controller can not only solve the periodic and aperiodic intermittent control, lower the update frequency of the controller, but also avoid the saturation phenomenon of impulsive control. Based on linear matrix inequalities (LMIs), and Jensen’s inequality, under a proposed suitable Lyapunov function, a series of sufficient conditions are established to guarantee the stability of the error system. Compared with the recent relevant impulsive saturation results, the polytopic representation method dealing with actuator saturation may make the synchronization criterion more universal and less restrictive. Finally, a numerical example is provided to verify the correctness and feasibility of the theoretical results.

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Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

Measurement and Control ◽

10.1177/0020294019893056 ◽

2020 ◽

Vol 53 (3-4) ◽

pp. 378-389 ◽

Cited By ~ 1

Author(s):

Weiyuan Zhang ◽

Junmin Li ◽

Jinghan Sun ◽

Minglai Chen

Keyword(s):

Neural Networks ◽

Feedback Control ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Linear Matrix ◽

Output Coupling ◽

Delayed Reaction ◽

Adaptive Feedback ◽

Adaptive Feedback Control ◽

Stochastic Synchronization

In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.

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Exponential Stabilization of Coupled Hybrid Stochastic Delayed BAM Neural Networks: A Periodically Intermittent Control Method

Complexity ◽

10.1155/2018/1708935 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14

Author(s):

Yunjian Peng ◽

Birong Zhao ◽

Weijie Sun ◽

Feiqi Deng

Keyword(s):

Neural Networks ◽

Closed Loop ◽

Control Method ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Functional Method ◽

Exponential Stabilization ◽

Intermittent Control ◽

Analysis Techniques ◽

Basic Parameters

This paper considers exponential stabilization for a class of coupled hybrid stochastic delayed bidirectional associative memory neural networks (HSD-BAM-NN) with reaction-diffusion terms. A periodically intermittent controller is proposed to exponentially stabilize such an unstable HSD-BAM-NN, and sufficient conditions of the closed-loop BAM-NN system with exponential stabilization are derived by using Lyapunov-Krasovskii functional method, stochastic analysis techniques, and integral inequality property, which decide the basic parameters of the proposed controller. Furthermore, a framework to establish simulation algorithm with sampled states is presented to implement the stabilization controller. With a HSD-BAM-NN model of power synchronization in a photovoltaic (PV) array field, we illustrate numerical simulation results to verify the correctness and effectiveness of the proposed controller.

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Exponential synchronization of inertial reaction-diffusion coupled neural networks with proportional delay via periodically intermittent control

Neurocomputing ◽

10.1016/j.neucom.2019.05.028 ◽

2019 ◽

Vol 356 ◽

pp. 195-205 ◽

Cited By ~ 4

Author(s):

Peng Wan ◽

Dihua Sun ◽

Dong Chen ◽

Min Zhao ◽

Linjiang Zheng

Keyword(s):

Neural Networks ◽

Reaction Diffusion ◽

Exponential Synchronization ◽

Proportional Delay ◽

Intermittent Control ◽

Periodically Intermittent Control ◽

Coupled Neural Networks

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Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

Journal of Applied Mathematics ◽

10.1155/2014/305264 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yang Fang ◽

Kang Yan ◽

Kelin Li

Keyword(s):

Neural Networks ◽

Impulsive Control ◽

Sufficient Conditions ◽

Stability Theorem ◽

Linear Matrix ◽

Matrix Inequality ◽

Lyapunov Stability Theorem ◽

Delayed Neural Networks ◽

Impulsive Synchronization ◽

Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

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Synchronization of delayed neural networks with hybrid coupling via impulsive control

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219834993 ◽

2019 ◽

Vol 41 (13) ◽

pp. 3714-3724 ◽

Cited By ~ 1

Author(s):

Tianhu Yu ◽

Huamin Wang ◽

Dengqing Cao

Keyword(s):

Neural Networks ◽

Linear Matrix Inequalities ◽

Upper Bound ◽

Hybrid Control ◽

Impulsive Control ◽

Distributed Delay ◽

Linear Matrix ◽

Matrix Inequalities ◽

Delayed Neural Networks ◽

Coupled Neural Networks

The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.

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Exponential Synchronization of Stochastic Reaction-Diffusion Fuzzy Cohen-Grossberg Neural Networks With Time-Varying Delays Via Periodically Intermittent Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4025157 ◽

2013 ◽

Vol 135 (6) ◽

Cited By ~ 5

Author(s):

Qintao Gan ◽

Yang Li

Keyword(s):

Neural Networks ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Exponential Synchronization ◽

Intermittent Control ◽

Time Varying ◽

Synchronization Problem ◽

Diffusion Effects ◽

Stochastic Reaction ◽

Delay Partitioning

In this paper, the exponential synchronization problem for fuzzy Cohen-Grossberg neural networks with time-varying delays, stochastic noise disturbance, and reaction-diffusion effects are investigated. By introducing a novel Lyapunov-Krasovskii functional with the idea of delay partitioning, a periodically intermittent controller is developed to derive sufficient conditions ensuring the addressed neural networks to be exponentially synchronized in terms of p-norm. The results extend and improve upon earlier work. A numerical example is provided to show the effectiveness of the proposed theories.

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Extended dissipative-based state estimation for Markov jump coupled neural networks with reaction-diffusion terms

Transactions of the Institute of Measurement and Control ◽

10.1177/01423312211028217 ◽

2021 ◽

pp. 014233122110282

Author(s):

Dongxiao Hu ◽

Xiaona Song ◽

Xingru Li

Keyword(s):

Neural Networks ◽

State Estimation ◽

Dynamic Error ◽

Signal Transmission ◽

Reaction Diffusion ◽

Linear Matrix ◽

Markov Jump ◽

Memory Controller ◽

Coupled Neural Networks ◽

Error System

This work mainly concentrates on the state estimation for Markov jump coupled neural networks (MJCNNs) with reaction-diffusion terms, in which the memory controller is employed. First, the considered MJCNNs model is introduced, and the dynamic error system can be obtained based on the proposed state estimator. Then, a memory controller that involves constant signal transmission delay is designed. Moreover, by Lyapunov functional method, inequality technique and Kronecker product law, a novel stable and extended dissipative analysis criteria can be established to ensure that the stability of the error system the error system. Meanwhile, the controller gains can be obtained by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

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Global synchronization for hybrid coupled neural networks with interval time-varying delays: A matrix-based quadratic convex approach

Asian-European Journal of Mathematics ◽

10.1142/s1793557117500255 ◽

2016 ◽

Vol 10 (02) ◽

pp. 1750025

Author(s):

Thongchai Botmart ◽

Narongsak Yotha ◽

Kanit Mukdasai ◽

Supreecha Wongaree

Keyword(s):

Neural Networks ◽

Time Derivative ◽

Sufficient Conditions ◽

Upper And Lower Bounds ◽

Linear Matrix ◽

Time Varying ◽

Global Synchronization ◽

Interval Time ◽

Coupled Neural Networks ◽

Time Varying Delay

This paper is concerned with the global synchronization problems for coupled neural networks (NNs) with hybrid coupling and interval time-varying delays. An appropriate Lyapunov–Krasovskii functional (LKF) and Kronecker product properties are used to form some new delay-dependent synchronization conditions in terms of linear matrix inequalities. A matrix-based quadratic convex approach introduce for sufficient conditions to ensure global synchronization where the time-varying delay is continuous uniformly bounded and its time-derivative bounded by upper and lower bounds. Simulation results are given to show the effectiveness and benefits of the proposed methods.

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Lag Synchronization of Coupled Delayed Chaotic Neural Networks by Periodically Intermittent Control

Abstract and Applied Analysis ◽

10.1155/2013/501461 ◽

2013 ◽

Vol 2013 ◽

pp. 1-5 ◽

Cited By ~ 4

Author(s):

Songjian Dan ◽

Simon X. Yang ◽

Wei Feng

Keyword(s):

Neural Networks ◽

Time Delay ◽

Sufficient Conditions ◽

Lyapunov Stability Theory ◽

Intermittent Control ◽

Lag Synchronization ◽

Chaotic Neural Networks ◽

Coupled Neural Networks ◽

Error System ◽

Delayed Chaotic Neural Networks

We investigate the lag synchronization of coupled neural networks with time delay. Some sufficient conditions for lag synchronization will be derived by using Lyapunov stability theory and intermittent control. Compared to existing results, some less conservative conditions are derived to guarantee the stabilization of error system. The analytical results are confirmed by numerical simulations.

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