scholarly journals Exponential synchronization control of delayed memristive neural network based on canonical Bessel-Legendre inequality

2022 ◽  
Vol 7 (3) ◽  
pp. 4711-4734
Author(s):  
Xingxing Song ◽  
◽  
Pengfei Zhi ◽  
Wanlu Zhu ◽  
Hui Wang ◽  
...  
Keyword(s):  
Exponential Synchronization ◽  
Synchronization Control ◽  
Intermittent Control ◽  
Parameter Mismatch ◽  
Synchronization Problem ◽  
Control Gain ◽  
Control Scheme ◽  
Vector Information ◽  
Memristive Neural Network ◽  
The Stability

<abstract><p>In this paper, we study the exponential synchronization problem of a class of delayed memristive neural networks(MNNs). Firstly, a intermittent control scheme is designed to solve the parameter mismatch problem of MNNs. A discontinuous controller with two tunable scalars is designed, and the upper limit of control gain can be adjusted flexibly. Secondly, an augmented Lyaponov-Krasovskii functional(LKF) is proposed, and vector information of N-order canonical Bessel-Legendre(B-L) inequalities is introduced. LKF method is used to obtain the stability criterion to ensure exponential synchronization of the system. The conservatism of the result decreases with the increase of the order of the B-L inequality. Finally, the effectiveness of the main results is verified by two simulation examples.</p></abstract>

Exponential synchronization in complex-variable network with distributed delays via intermittent control

2017 ◽  
Vol 28 (07) ◽  
pp. 1750089 ◽  
Author(s):  
Sulan He ◽  
Guisheng Yi ◽  
Zhaoyan Wu
Keyword(s):  
Complex Variable ◽  
Exponential Synchronization ◽  
Distributed Delays ◽  
Intermittent Control ◽  
Control Gain ◽  
Analysis Technique ◽  
Control Scheme ◽  
Lyapunov Function Method ◽  
And Control ◽  
Theoretical Results

In this paper, exponential synchronization in complex-variable network with distributed delays is investigated. By utilizing intermittent control scheme, some effective controllers are designed. Based on the Lyapunov function method and mathematical analysis technique, some synchronization criteria with respect to the system parameters, control gain and control rate are presented. From the criteria, for any given dynamical network, the needed values of control gains and rate can be easily estimated. Finally, two numerical simulations are performed to verify the derived theoretical results.

scholarly journals Adaptive Aperiodically Intermittent Synchronization for Complex Dynamical Network with Unknown Time-Varying Outer Coupling Strengths

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Lihong Yan ◽  
Junmin Li
Keyword(s):  
Adaptive Learning ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Time Varying ◽  
Complex Dynamical Network ◽  
Dynamical Network ◽  
Synchronization Problem ◽  
Coupling Strengths ◽  
Inequality Techniques ◽  
Theoretical Results

In this paper, exponential synchronization problem of complex dynamical networks with unknown periodically coupling strengths was investigated. An aperiodically intermittent control synchronization strategy is proposed. Based on Lyapunov exponential stability theory, inequality techniques, and adaptive learning laws design, some sufficient exponential synchronization criteria for complex dynamical network with unknown periodical coupling weights are obtained. The numerical simulation example is presented to illustrate the feasibility of theoretical results.

scholarly journals Exponential Synchronization of Inertial Cohen–Grossberg Neural Networks with Time-Varying Delays via Periodically Intermittent Control

2020 ◽  
Vol 15 (2) ◽  
pp. 15
Author(s):  
Qing Ding ◽  
Yinfang Song
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Exponential Synchronization ◽  
Intermittent Control ◽  
Time Varying ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Control Schemes ◽  
Inequality Techniques

This paper deals with the exponential synchronization problem of inertial Cohen–Grossberg neural networks with time-varying delays under periodically intermittent control. In light of Lyapunov–Krasovskii functional method and inequality techniques, some sufficient conditions are attained to ensure the exponential synchronization of the master-slave system on the basis of p-norm. Meanwhile, the periodically intermittent control schemes are designed. Finally, in order to verify the effectiveness of theoretical results, some numerical simulations are provided.

scholarly journals Stability of delay neural networks with uncertainties via delayed intermittent control

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yujuan Tian ◽  
Fei Wang ◽  
Yao Wang ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
Asymptotical Stability ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Weighting Matrix ◽  
Control Scheme ◽  
Globally Asymptotical Stability ◽  
The Stability ◽  
Delay Dependent

Abstract In this paper, we investigate the stability of neural networks with both time-varying delays and uncertainties. A novel delayed intermittent control scheme is designed to ensure the globally asymptotical stability of the addressed system. Some new delay dependent sufficient criteria for globally asymptotical stability results are derived in term of linear matrix inequalities (LMIs) by using free-weighting matrix techniques and Lyapunov–Krasovskii functional method. Finally, a numerical simulation is provided to show the effectiveness of the proposed approach.

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

2013 ◽  
Vol 135 (6) ◽  
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.

scholarly journals Stochastically exponential synchronization for Markov jump neural networks with time-varying delays via event-triggered control scheme

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaoman Liu ◽  
Haiyang Zhang ◽  
Jun Yang ◽  
Hao Chen
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Analytical Techniques ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Markov Jump ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Reciprocally Convex Combination ◽  
Event Triggered

AbstractThis paper focuses on the stochastically exponential synchronization problem for one class of neural networks with time-varying delays (TDs) and Markov jump parameters (MJPs). To derive a tighter bound of reciprocally convex quadratic terms, we provide an improved reciprocally convex combination inequality (RCCI), which includes some existing ones as its particular cases. We construct an eligible stochastic Lyapunov–Krasovskii functional to capture more information about TDs, triggering signals, and MJPs. Based on a well-designed event-triggered control scheme, we derive several novel stability criteria for the underlying systems by employing the new RCCI and other analytical techniques. Finally, we present two numerical examples to show the validity of our methods.

scholarly journals Pinning Adaptive Synchronization of Delayed Coupled Dynamical Networks via Periodically Intermittent Control

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xueliang Liu ◽  
Shengbing Xu
Keyword(s):  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Adaptive Synchronization ◽  
Intermittent Control ◽  
Dynamical Networks ◽  
Adaptive Feedback ◽  
Periodically Intermittent Control ◽  
Synchronization Problem ◽  
Theoretical Results

This paper investigates the exponential synchronization problem of delayed coupled dynamical networks by using adaptive pinning periodically intermittent control. Based on the Lyapunov method, by designing adaptive feedback controller, some sufficient conditions are presented to ensure the exponential synchronization of coupled dynamical networks with delayed coupling. Furthermore, a numerical example is given to demonstrate the validity of the theoretical results.

scholarly journals Robust Synchronization of the Unified Chaotic System

2015 ◽  
Vol 5 (1) ◽  
pp. 102
Author(s):  
Hatem Trabelsi ◽  
Mohamed Benrejeb
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Synchronization Control ◽  
Compound Matrices ◽  
Synchronization Problem ◽  
Unified Chaotic System ◽  
Unified Chaotic Systems ◽  
Robust Synchronization ◽  
Control Scheme ◽  
Unknown System

<p>The paper investigates the synchronization problem of the unified chaotic system. The case of identical, but unknown master and slave unified chaotic systems is considered. Based on compound matrices formalism, a unified synchronization control scheme is proposed independently of the unknown system parameter. Simulation results are provided to show the effectiveness of the presented scheme.</p>

scholarly journals Impulsive Synchronization of Nonlinearly Coupled Complex Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Guizhen Feng ◽  
Jinde Cao ◽  
Jianquan Lu
Keyword(s):  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Sufficient Condition ◽  
Impulsive Synchronization ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Objective State ◽  
The Stability ◽  
Low Dimensional ◽  
Average Impulsive Interval

This paper investigates synchronization problem of nonlinearly coupled dynamical networks, and an effectively impulsive control scheme is proposed to synchronize the network onto the objective state. Based on the stability analysis of impulsive differential equations, a low-dimensional sufficient condition is derived to guarantee the exponential synchronization in virtual of average impulsive interval. A numerical example is given to illustrate the effectiveness and feasibility of the proposed methods and results.

Adaptive intermittent control for exponential synchronization of directed networks with complex-variable systems and distributed delays coupling

2018 ◽  
Vol 29 (11) ◽  
pp. 1850110 ◽  
Author(s):  
Shuiming Cai ◽  
Xiaojing Li ◽  
Feilong Zhou
Keyword(s):  
Complex Variable ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Distributed Delays ◽  
Control Technique ◽  
Intermittent Control ◽  
Directed Networks ◽  
Control Gain ◽  
Intermittent Feedback

In this paper, adaptive exponential synchronization of directed networks with complex-variable systems and distributed delays coupling is investigated. An adaptive nonperiodical intermittent control scheme is adopted to realize exponential synchronization of such complex-variable directed dynamical networks. Based on the complex inequality, piecewise analysis method and Lyapunov stability theory, some sufficient conditions guaranteeing globally exponential synchronization are established. Different from previous works, here the designed adaptive update law for intermittent feedback control gain does not explicitly depend on time, which makes the adaptive nonperiodical intermittent control technique more convenient to implement in realistic applications. Moreover, it is indicated that the established synchronization criteria depend on the control rates rather than the control periods or control widths, and therefore the control periods can be optionally chosen for practical problems. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results.

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