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

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.

scholarly journals Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hongwen Xu ◽  
Huaiqin Wu ◽  
Ning Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
State Estimation ◽  
Time Delays ◽  
Estimation Error ◽  
Linear Matrix ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Distributed Time Delays ◽  
Error System

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical 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 H-infinity State Estimation of Uncertain Neural Networks with Two Additive Time-Varying Delays

2020 ◽  
Author(s):  
Xiaoping Hu ◽  
Yajun Wang ◽  
Jiakai Ding ◽  
Dongming Xiao
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Uncertain Neural Networks ◽  
Error System

This study is mainly concerned with the problem of robust H∞ state estimation of uncertain neural networks with two additive time-varying delays. A novel linear matrix inequalities (LMIs) is constructed based on Lyapunov-Krasovskii functionals (LKFs) which contains two additive time-varying delays components. LMIs method are used to estimate the derivative of LKFs, it is calculated that the derivative of the LKFs is smaller than zero, which proved that uncertain neural networks with two additive time-varying delays is globally asymptotically stable. Meantime, a stability criterion of error system is presented such that the HâĹđ performance is guaranteed. Finally, two numerical simulation examples have been performed to demonstrate the effectiveness of developed approach.

scholarly journals Improved Results onH∞State Estimation of Static Neural Networks with Time Delay

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Bin Wen ◽  
Hui Li ◽  
Shouming Zhong
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
State Estimator ◽  
Static Neural Networks ◽  
Exponentially Stable ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

This paper studies the problem ofH∞state estimation for a class of delayed static neural networks. The purpose of the problem is to design a delay-dependent state estimator such that the dynamics of the error system is globally exponentially stable and a prescribedH∞performance is guaranteed. Some improved delay-dependent conditions are established by constructing augmented Lyapunov-Krasovskii functionals (LKFs). The desired estimator gain matrix can be characterized in terms of the solution to LMIs (linear matrix inequalities). Numerical examples are provided to illustrate the effectiveness of the proposed method compared with some existing results.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

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