scholarly journals Adaptive Cluster Synchronization of Complex Networks with Identical and Nonidentical Lur’e Systems

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 706
Author(s):  
Yue Gao ◽  
Dong Ding ◽  
Ze Tang
Keyword(s):  
Numerical Simulation ◽  
Continuous Function ◽  
Complex Networks ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Function Class ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Lur’E Systems ◽  
Control Schemes

This paper is devoted to investigating the cluster synchronization of a class of nonlinearly coupled Lur’e networks. A novel adaptive pinning control strategy is introduced, which is beneficial to achieve cluster synchronization of the Lur’e systems in the same cluster and weaken the directed connections of the Lur’e systems in different clusters. The coupled complex networks consisting of not only identical Lur’e systems but also nonidentical Lur’e systems are discussed, respectively. Based on the S-procedure and the concept of acceptable nonlinear continuous function class, sufficient conditions are obtained which prove that the complex dynamical networks can be pinned to the heterogeneous solutions for any initial values. In addition, effective and comparatively small control strengths are acquired by the designing of the adaptive updating algorithm. Finally, a numerical simulation is presented to illustrate the proposed theorems and the control schemes.

scholarly journals Cluster Synchronization for Linearly Coupled Complex Networks with Identical and Nonidentical Nodes

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yi Zhao ◽  
Jianwen Feng ◽  
Jingyi Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Adaptive Feedback ◽  
Numerical Examples ◽  
Control Schemes ◽  
Nonidentical Nodes ◽  
Theoretical Results

The cluster synchronization of linearly coupled complex networks with identical and nonidentical nodes is studied. Without assuming symmetry, we proved that these linearly coupled complex networks could achieve cluster synchronization under certain pinning control schemes. Sufficient conditions guaranteeing cluster synchronization for any initial values are derived by using Lyapunov function methods. Moreover, the adaptive feedback algorithms are proposed to adjust the control strength. Several numerical examples are given to illustrate our theoretical results.

The Control of a Neural Complex Network

2014 ◽  
Vol 687-691 ◽  
pp. 444-446
Author(s):  
Fan Di Zhang
Keyword(s):  
Neural Network ◽  
Community Structure ◽  
Lyapunov Stability ◽  
Control Strategy ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Projective Synchronization ◽  
Cluster Synchronization ◽  
Special Cases

In this paper, the synchronization of a neural network with community structure is investigated. Cluster projective generalizes previously existing synchronization schemes. The cluster projective synchronization is more general that includes projective synchronization and cluster synchronization, as its special cases. The cluster projective synchronization of these networks is discussed via some pinning control strategy. Several sufficient conditions for the network to achieve cluster projective synchronization are derived based on Lyapunov stability theory. Numerical simulations are used to demonstrate the effectiveness and feasibility of the proposed scheme.

scholarly journals The Effect of Control Strength on Lag Synchronization of Nonlinear Coupled Complex Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Shuguo Wang ◽  
Hongxing Yao
Keyword(s):  
Numerical Simulation ◽  
Complex Networks ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Lyapunov Direct Method ◽  
Lag Synchronization ◽  
Control Strength

This paper mainly investigates the lag synchronization of nonlinear coupled complex networks using methods that are based on pinning control, where the weight configuration matrix is not necessarily symmetric or irreducible. We change the control strength into a parameter concerning timet, by using the Lyapunov direct method, some sufficient conditions of lag synchronization are obtained. To validate the proposed method, numerical simulation examples are provided to verify the correctness and effectiveness of the proposed scheme.

scholarly journals Pinning Cluster Synchronization in Linear Hybrid Coupled Delayed Dynamical Networks

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Anping Bao ◽  
Ting Wang ◽  
Shumin Fei ◽  
Xiaomin Tian
Keyword(s):  
Control Strategy ◽  
Kronecker Product ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Dynamical Networks ◽  
Delayed Dynamical Networks

The problem on cluster synchronization will be investigated for a class of delayed dynamical networks based on pinning control strategy. Through utilizing the combined convex technique and Kronecker product, two sufficient conditions can be derived to ensure the desired synchronization when the designed feedback controller is employed to each cluster. Moreover, the inner coupling matrices are unnecessarily restricted to be diagonal and the controller design can be converted into solving a series of linear matrix inequalities (LMIs), which greatly improve the present methods. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism.

scholarly journals Outer Synchronization of Complex Networks with Nondelayed and Time-Varying Delayed Couplings via Pinning Control or Impulsive Control

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwen Feng ◽  
Sa Sheng ◽  
Ze Tang ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Time Varying ◽  
Network Nodes ◽  
Outer Synchronization ◽  
Synchronization Problem ◽  
Response Network ◽  
Control Schemes

The outer synchronization problem between two complex networks with nondelayed and time-varying delayed couplings via two different control schemes, namely, pinning control and impulsive control, is considered. Firstly, by applying pinning control to a fraction of the network nodes and using a suitable Lyapunov function, we obtain some new and useful synchronization criteria, which guarantee the outer synchronization between two complex networks. Secondly, impulsive control is added to the nodes of corresponding response network. Based on the generalized inequality about time-varying delayed different equation, the sufficient conditions for outer synchronization are derived. Finally, some examples are presented to demonstrate the effectiveness and feasibility of the results obtained in this paper.

scholarly journals Cluster Synchronization of Nonlinearly Coupled Complex Networks via Pinning Control

2011 ◽  
Vol 2011 ◽  
pp. 1-23 ◽  
Author(s):  
Jianwen Feng ◽  
Jingyi Wang ◽  
Chen Xu ◽  
Francis Austin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Coupling Strength ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
General Complex ◽  
Coupling Strengths ◽  
Theoretical Results

We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.

scholarly journals Cluster Synchronization of Stochastic Complex Networks with Markovian Switching and Time-Varying Delay via Impulsive Pinning Control

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xuan Zhou ◽  
Kui Luo
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Markovian Switching ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
Stochastic Complex Networks

This paper studies the cluster synchronization of a kind of complex networks by means of impulsive pinning control scheme. These networks are subject to stochastic noise perturbations and Markovian switching, as well as internal and outer time-varying delays. Using the Lyapunov-Krasovskii functional, Itö’s formula, and some linear matrix inequalities (LMI), several novel sufficient conditions are obtained to guarantee the desired cluster synchronization. At the end of this writing, a numerical simulation is given to demonstrate the effectiveness of those theoretical results.

scholarly journals Adaptive Cluster Synchronization for Nondelayed and Delayed Coupling Complex Networks with Nonidentical Nodes

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Sufficient Conditions ◽  
Pinning Control ◽  
Cluster Synchronization ◽  
Linear Matrix ◽  
Control Cost ◽  
Synchronization Problem ◽  
Delayed Coupling ◽  
Control Scheme ◽  
Successful Control ◽  
Synchronization Pattern

We focus on the cluster synchronization problem for a kind of general networks with nondelayed and delayed coupling. Based on the pinning control scheme, a small fraction of the nodes in each cluster are pinned for successful control, and the states of the whole dynamical networks can be globally forced to the objective cluster states. Sufficient conditions are derived to guarantee the realization of the cluster synchronization pattern for all initial values by means of the Lyapunov stability theorem and linear matrix inequalities (LMIs). By using the adaptive update law, relative smaller control gains are obtained, and hence the control cost can be substantially lower. Numerical simulations are also exploited to demonstrate the effectiveness and validity of the main result.

Sign in / Sign up

Export Citation Format

Share Document