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

Complexity ◽  
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.

Exponential Stability of Stochastic Reaction-Diffusion Neural Networks with Mixed Delays in Procurement of Maintenance Material

2011 ◽  
Vol 105-107 ◽  
pp. 2315-2320
Author(s):  
Xiao Chen
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Exponential Stability ◽  
Effective Means ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Mixed Delays ◽  
The Neural Network ◽  
Discrete Time Delay

In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

Exponential Stabilization of Delayed Chaotic Memristive Neural Networks Via Aperiodically Intermittent Control

2020 ◽  
Vol 30 (02) ◽  
pp. 2050029
Author(s):  
Yuxia Li ◽  
Li Wang ◽  
Xia Huang
Keyword(s):  
Neural Networks ◽  
Closed Loop ◽  
Control Period ◽  
Exponential Stabilization ◽  
Interval Matrix ◽  
Feedback Gain ◽  
Intermittent Control ◽  
Memristive Neural Networks ◽  
Control Cost ◽  
The Relationship

This paper investigates the exponential stabilization of delayed chaotic memristive neural networks (MNNs) via aperiodically intermittent control. The issue is proposed for two reasons: (1) The control signal may not always exist in practical applications; (2) How to enlarge the maximum allowable failure interval (MAFI) for sensors is a challenging problem. To surmount these difficulties, an index called the largest proportion of the rest width (LPRW) in the control period is proposed to measure the MAFI in the sense of guaranteeing the closed-loop system performance with the least control cost. Then, by constructing suitable Lyapunov functional in combination with interval matrix method and Halanay inequality, a stabilization criterion is established to determine the relationship between the feedback gain and the LPRW. Meanwhile, an algorithm is proposed to qualitatively analyze the relationship between the feedback gain and the LPRW. In contrast with the previous works, our results can increase the value of LPRW while still maintaining the stability of the closed-loop MNNs. Finally, some comparisons of simulation results demonstrate that the obtained stabilization criterion has some advantages over the existing ones.

scholarly journals Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He ◽  
Lehua Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Distributed Delays ◽  
Almost Sure Exponential Stability ◽  
Mean Square Exponential Stability ◽  
Stochastic Reaction

Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.

scholarly journals Passivity Analysis of Coupled Stochastic Neural Networks with Multiweights

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Min Cao ◽  
Xun-Wu Yin ◽  
Wen-He Song ◽  
Xue-Mei Sun ◽  
Cheng-Dong Yang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Analysis Techniques ◽  
Passivity Analysis ◽  
Input And Output ◽  
Lyapunov Functional Method ◽  
Theoretical Results

In this paper, we devote to the investigation of passivity in two types of coupled stochastic neural networks (CSNNs) with multiweights and incompatible input and output dimensions. First, some new definitions of passivity are proposed for stochastic systems that may have incompatible input and output dimensions. By utilizing stochastic analysis techniques and Lyapunov functional method, several sufficient conditions are respectively developed for ensuring that CSNNs without and with multiple delay couplings can realize passivity. Besides, the synchronization criteria for CSNNs with multiweights are established by employing the results of output-strictly passivity. Finally, two simulation examples are given to illustrate the validity of the 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.

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 Stochastic Synchronization of Reaction-Diffusion Neural Networks under General Impulsive Controller with Mixed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Xinsong Yang ◽  
Chuangxia Huang ◽  
Zhichun Yang
Keyword(s):  
Neural Networks ◽  
Control Method ◽  
Mathematical Proof ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Mixed Delays ◽  
Multiple Time ◽  
Time Varying ◽  
Stochastic Perturbations

This paper investigates drive-response synchronization of a class of reaction-diffusion neural networks with time-varying discrete and distributed delays via general impulsive control method. Stochastic perturbations in the response system are also considered. The impulsive controller is assumed to be nonlinear and has multiple time-varying discrete and distributed delays. Compared with existing nondelayed impulsive controller, this general impulsive controller is more practical and essentially important since time delays are unavoidable in practical operation. Based on a novel impulsive differential inequality, the properties of random variables and Lyapunov functional method, sufficient conditions guaranteeing the global exponential synchronization in mean square are derived through strict mathematical proof. In our synchronization criteria, the distributed delays in both continuous equation and impulsive controller play important role. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

scholarly journals Novel Criteria on Global Robust Exponential Stability to a Class of Reaction-Diffusion Neural Networks with Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Pan ◽  
Shouming Zhong
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Compact Sets ◽  
Robust Exponential Stability ◽  
Delayed Neural Networks ◽  
Global Exponential Robust Stability

The global exponential robust stability is investigated to a class of reaction-diffusion Cohen-Grossberg neural network (CGNNs) with constant time-delays, this neural network contains time invariant uncertain parameters whose values are unknown but bounded in given compact sets. By employing the Lyapunov-functional method, several new sufficient conditions are obtained to ensure the global exponential robust stability of equilibrium point for the reaction diffusion CGNN with delays. These sufficient conditions depend on the reaction-diffusion terms, which is a preeminent feature that distinguishes the present research from the previous research on delayed neural networks with reaction-diffusion. Two examples are given to show the effectiveness of the obtained results.

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

2021 ◽  
pp. 2150398
Author(s):  
Zhengran Cao ◽  
Chuandong Li ◽  
Zhilong He ◽  
Xiaoyu Zhang
Keyword(s):  
Neural Networks ◽  
Actuator Saturation ◽  
Impulsive Control ◽  
Input Saturation ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Intermittent Control ◽  
Coupled Neural Networks ◽  
Hybrid Controller

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.

scholarly journals Robust Exponential Stabilization of Stochastic Delay Interval Recurrent Neural Networks with Distributed Parameters and Markovian Jumping by Using Periodically Intermittent Control

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Junhao Hu ◽  
Yunjian Peng ◽  
Yan Li
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Exponential Stabilization ◽  
Intermittent Control ◽  
Markovian Jumping ◽  
Stochastic Delay ◽  
Periodically Intermittent Control ◽  
Distributed Parameters ◽  
Robust Exponential Stabilization

We consider a class of stochastic delay recurrent neural networks with distributed parameters and Markovian jumping. It is assumed that the coefficients in these neural networks belong to the interval matrices. Several sufficient conditions ensuring robust exponential stabilization are derived by using periodically intermittent control and Lyapunov functional. The obtained results are very easy to verify and implement, and improve the existing results. Finally, an example with numerical simulations is given to illustrate the presented criteria.

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