scholarly journals Robust Fixed-Time Synchronization for Coupled Delayed Neural Networks with Discontinuous Activations Subject to a Quadratic Polynomial Growth

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lina Yu ◽  
Yunfei Ma ◽  
Yuntong Yang ◽  
Jingchao Zhang ◽  
Chunwei Wang
Keyword(s):  
Neural Networks ◽  
Time Synchronization ◽  
Fixed Time ◽  
Functional Method ◽  
Quadratic Polynomial ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Analysis Technique ◽  
Discontinuous Activations ◽  
Discontinuous Activation Functions

In this paper, we focus on the robust fixed-time synchronization for discontinuous neural networks (NNs) with delays and hybrid couplings under uncertain disturbances, where the growth of discontinuous activation functions is governed by a quadratic polynomial. New state-feedback controllers, which include integral terms and discontinuous factors, are designed. By Lyapunov–Krasovskii functional method and inequality analysis technique, some sufficient criteria, which ensue that networks can realize the robust fixed-time synchronization, are addressed in terms of linear matrix inequalities (LMIs). Moreover, the upper bound of the settling time, which is independent on the initial values, can be determined to any desired values in advance by the configuration of parameters in the proposed control law. Finally, two examples are provided to illustrate the validity of the theoretical results.

COMPLETE PERIODIC SYNCHRONIZATION OF DELAYED NEURAL NETWORKS WITH DISCONTINUOUS ACTIVATIONS

2010 ◽  
Vol 20 (07) ◽  
pp. 2151-2164 ◽  
Author(s):  
XIAOYANG LIU ◽  
JINDE CAO ◽  
GAN HUANG
Keyword(s):  
Neural Networks ◽  
Control Method ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Discontinuous Activations ◽  
Potential Applications ◽  
Error System ◽  
Discontinuous Activation Functions ◽  
Necessary And Sufficient ◽  
Theoretical Results

Recently, the synchronization issue in chaotic systems has become a hot topic in nonlinear dynamics and has aroused great interest among researchers due to the theoretical significance and potential applications. In this paper, complete periodic synchronization is considered for the delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution, a novel control method is presented by using differential inclusions theory, nonsmooth Lyapunov method and linear matrix inequality (LMI) approach. Based on a newly obtained necessary and sufficient condition, several criteria are derived to ensure the global asymptotical stability of the error system, and thus the response system synchronizes with the drive system. Moreover, the estimation gains are obtained. With these new and effective methods, complete synchronization is achieved. Simulation results are given to illustrate the theoretical results.

scholarly journals Global Finite-Time and Fixed-Time Synchronization for Discontinuous Complex Dynamical Networks with Semi-Markovian Switching and Mixed Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Lina Yu ◽  
Jingchao Zhang ◽  
Yunfei Ma ◽  
Xinhua Tan ◽  
Chunwei Wang
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Fixed Time ◽  
Functional Method ◽  
Markovian Switching ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Dynamical Networks ◽  
Analysis Technique

This paper is concerned with the global finite-time and fixed-time synchronization for a class of discontinuous complex dynamical networks with semi-Markovian switching and mixed time-varying delays. The novel state-feedback controllers, which include integral terms and discontinuous facts, are designed to realize the global synchronization between the drive system and response system. By applying the Lyapunov functional method and matrix inequality analysis technique, the global finite-time and fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

scholarly journals Fixed-time control of delayed neural networks with impulsive perturbations

2018 ◽  
Vol 23 (6) ◽  
pp. 904-920 ◽  
Author(s):  
Jingting Hu ◽  
Guixia Sui ◽  
Xiaoxiao Lv ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Initial Conditions ◽  
Fixed Time ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Time Control ◽  
Analysis Technique ◽  
Lyapunov Function Method ◽  
Impulsive Perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis.

scholarly journals The Fast Fixed-Time Bipartite Synchronization of Coupled Delayed Neural Networks with Signed Graphs

2021 ◽  
Author(s):  
Shiju Yang ◽  
Chuandong Li ◽  
Yu Li ◽  
Ting Yang ◽  
Bo Li
Keyword(s):  
Neural Networks ◽  
Time Synchronization ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Initial Condition ◽  
Signed Graphs ◽  
Comparison System ◽  
Delayed Neural Networks ◽  
Synchronization Problem ◽  
System Method

Abstract In this paper, the fixed-time bipartite synchronization problem for coupled delayed neural networks with signed graphs is discussed. Different from traditional neural networks, the interactions between nodes of delayed neural networks can be either collaborative or antagonistic. Furthermore, compared with the initial-condition based finite-time synchronization, the settling time is bounded by a constant within fixedtime regardless of the initial condition. It is worth noting that the fixed-time stable network for bipartite synchronization in this paper achieves more faster convergence than most existing publications. By applying constructing comparison system method, Lyapunov stability theory and inequality techniques, some sufficient criteria for fixed-time bipartite synchronization are obtained. Finally, two numerical examples are granted to display the performance of the obtained results.

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

2018 ◽  
Vol 20 (6) ◽  
pp. 2237-2247 ◽  
Author(s):  
Enli Wu ◽  
Xinsong Yang ◽  
Chen Xu ◽  
Fuad E. Alsaadi ◽  
Tasawar Hayat
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Delayed Neural Networks ◽  
Discontinuous Activations ◽  
Complex Valued
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