Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications

2017 ◽  
Vol 40 (10) ◽  
pp. 3078-3087 ◽  
Author(s):  
Xiaona Song ◽  
Shuai Song ◽  
Bo Li ◽  
Ines Tejado Balsera
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Hybrid Control ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Secure Communications ◽  
Uncertain Parameters ◽  
Matrix Inequalities

In this paper, the adaptive projective synchronization of time-delayed fractional-order neural networks is considered. Using the active control and adaptive control methods, efficient hybrid control strategies are designed for time-delayed fractional-order neural networks with uncertain parameters. Based on a new version of fractional-order Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities, which is easily checked and applied to practical systems. Finally, numerical simulations and application of the proposed methods to secure communications have been presented to validate the synchronization method.

Synchronization of delayed neural networks with hybrid coupling via impulsive control

2019 ◽  
Vol 41 (13) ◽  
pp. 3714-3724 ◽  
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.

scholarly journals LMI-Based Stability Criteria for Discrete-Time Neural Networks with Multiple Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hui Xu ◽  
Ranchao Wu
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Discrete Model ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Neural Models

Discrete neural models are of great importance in numerical simulations and practical implementations. In the current paper, a discrete model of continuous-time neural networks with variable and distributed delays is investigated. By Lyapunov stability theory and techniques such as linear matrix inequalities, sufficient conditions guaranteeing the existence and global exponential stability of the unique equilibrium point are obtained. Introduction of LMIs enables one to take into consideration the sign of connection weights. To show the effectiveness of the method, an illustrative example, along with numerical simulation, is presented.

scholarly journals Passivity analysis of multiple time-varying time delayed complex variable neural networks in finite-time

2021 ◽  
Vol 8 (4) ◽  
pp. 842-854
Author(s):  
N. Jayanthi ◽  
◽  
R. Santhakumari ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Complex Valued ◽  
Theoretical Results

In this article, we investigate the problem of finite-time passivity for the complex-valued neural networks (CVNNs) with multiple time-varying delays. To begin, many definitions relevant to the finite-time passivity of CVNNs are provided; then the suitable control inputs are designed to guarantee the class of CVNNs are finite-time passive. In the meantime, some sufficient conditions of linear matrix inequalities (LMIs) are derived by using inequalities techniques and Lyapunov stability theory. Finally, a numerical example is presented to illustrate the usefulness of the theoretical results.

New criteria for dissipativity analysis of Caputo fractional-order neural networks with non-differentiable time-varying delays

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Nguyen Thi Phuong ◽  
Nguyen Thi Thanh Huyen ◽  
Nguyen Thi Huyen Thu ◽  
Nguyen Huu Sau ◽  
Mai Viet Thuan
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Simulation Results ◽  
Delay Dependent ◽  
Dissipativity Analysis ◽  
New Criteria

Abstract In this article, we investigate the delay-dependent and order-dependent dissipativity analysis for a class of Caputo fractional-order neural networks (FONNs) subject to time-varying delays. By employing the Razumikhin fractional-order (RFO) approach combined with linear matrix inequalities (LMIs) techniques, a new sufficient condition is derived to guarantee that the considered fractional-order is strictly (Q, S, R) − γ − dissipativity. The condition is presented via LMIs and can be efficiently checked. Two numerical examples and simulation results are finally provided to express the effectiveness of the obtained results.

scholarly journals Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Fengjiao Wu ◽  
Guitao Zhang ◽  
Zhengzhong Wang
Keyword(s):  
Fuzzy Control ◽  
Fractional Order ◽  
Matrix Theory ◽  
Control Method ◽  
Interval Matrix ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequalities ◽  
Random Disturbances ◽  
The Stability

The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.

Modified function projective synchronization between two different complex networks with delayed couplings and delayed nodes of different dimensions

2016 ◽  
Vol 27 (11) ◽  
pp. 1650126 ◽  
Author(s):  
Min Han ◽  
Yamei Zhang ◽  
Meng Zhang
Keyword(s):  
Hybrid Control ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Linear Matrix ◽  
Function Projective Synchronization ◽  
Special Cases ◽  
Modified Function Projective Synchronization ◽  
Different Dimensions ◽  
Nodes Of Different Dimensions

In this paper, to deal with the problem of modified function projective synchronization (MFPS) between two different networks with delayed couplings and delayed nodes of different dimensions, a hybrid control scheme combining adaptive control and nonlinear control is proposed. First, a more realistic drive-response complex network model is constructed by introducing double delays. Then, we design hybrid feedback controllers to synchronize up the drive and response networks of different dimensions to a scaling function matrix. Based on Lyapunov stability theory and the linear matrix inequality (LMI), we rigorously prove that the MFPS between the proposed drive-response networks can be achieved and meanwhile some sufficient conditions are derived by adopting an appropriate Lyapunov–Krasovskii energy function. Noteably, many existing synchronization settings can be regarded as special cases of the present synchronization framework. Numerical simulation experiments are employed to verify the correctness and the effectiveness of the proposed method.

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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