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 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.

A DEGREE-BASED STRATEGY FOR CONSTRAINED PINNING CONTROL OF COMPLEX NETWORKS

2010 ◽  
Vol 20 (05) ◽  
pp. 1533-1539 ◽  
Author(s):  
WALLACE K. S. TANG ◽  
KA-HO NG ◽  
QIANG JIA
Keyword(s):  
Complex Networks ◽  
Optimization Problem ◽  
Pinning Control ◽  
Constrained Control ◽  
Effective Solution ◽  
Constrained Optimization Problem ◽  
Control Effect ◽  
Control Strength ◽  
Strategy Design ◽  
Pinning Strategy

In this paper, a modified degree-based strategy is proposed for pinning control of complex networks under constrained control capacity. Limited by the total control strength, the pinning strategy design problem is reconsidered as a constrained optimization problem. To provide a fast and effective solution, a decrease-and-conquer approach has been designed to assign the best control strengths to the pinned highest-degree nodes. Simulation results have demonstrated that the obtained strategy provides an outperformed control effect on various kinds of complex networks, as compared with strategies derived from degree, betweenness or closeness using evenly-distributed control strength.

scholarly journals Synchronization of Complex Networks with Time-Varying Delayed Dynamical Nodes via Pinning Control

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Shuguo Wang ◽  
Hongxing Yao ◽  
Qiuxiang Bian
Keyword(s):  
Numerical Simulation ◽  
Complex Networks ◽  
Pinning Control ◽  
Effective Control ◽  
Time Varying ◽  
Time Varying Delay ◽  
Control Scheme ◽  
Adaptive Coupling ◽  
Coupling Strengths ◽  
Varying Delay

This paper investigates the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delay and time-varying delay in dynamical nodes. Some simple and useful criteria are derived by constructing an effective control scheme and adjusting automatically the adaptive coupling strengths. To validate the proposed method, numerical simulation examples are provided to verify the correctness and effectiveness of the proposed scheme.

Global stabilization of memristor-based fractional-order neural networks with delay via output-feedback control

2017 ◽  
Vol 31 (05) ◽  
pp. 1750031 ◽  
Author(s):  
Jiyang Chen ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Xujun Yang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Output Feedback ◽  
Differential Inclusions ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Global Stabilization ◽  
Lyapunov Direct Method ◽  
Stabilizing Control

In this paper, the memristor-based fractional-order neural networks (MFNN) with delay and with two types of stabilizing control are described in detail. Based on the Lyapunov direct method, the theories of set-value maps, differential inclusions and comparison principle, some sufficient conditions and assumptions for global stabilization of this neural network model are established. Finally, two numerical examples are presented to demonstrate the effectiveness and practicability of the obtained results.

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.

scholarly journals Parameter Estimation and Hybrid Lag Synchronization in Hyperchaotic Lü Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qing Wei ◽  
Zuolei Wang
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Adaptive Control ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Lag Synchronization ◽  
Control Approach ◽  
Simulation Results

The antiphase and complete lag synchronization of hyperchaotic Lü systems with unknown parameters is investigated. Based on the Lyapunov stability theory, the sufficient conditions for achieving hybrid lag synchronization are derived. The optimized parameter observers are approached analytically via adaptive control approach. Numerical simulation results are presented to verify the effectiveness of the proposed scheme.

Design and Simulation of Robust and Adaptive Controls for a Nonlinear String System1

2004 ◽  
Vol 126 (1) ◽  
pp. 54-62
Author(s):  
Weiwei Jin ◽  
Zhihua Qu ◽  
Kuo-Chi Lin
Keyword(s):  
Numerical Simulation ◽  
Vibration Control ◽  
Boundary Control ◽  
Closed Loop ◽  
Direct Method ◽  
Closed Loop System ◽  
Lyapunov Direct Method ◽  
Adaptive Controls ◽  
Control Designs ◽  
Nonlinear String

In this paper, vibration control of a nonlinear string system is considered. The system consists of a nonlinear string, two boundary supporting mechanisms, and a moving transporter at the base. To suppress the vibration, boundary control designs are carried out. A new robust and adaptive boundary controller is designed using the Lyapunov direct method. The proposed control is implemented at the two ends supporting the string to compensate for vibration induced by the base motion. It is shown that the adaptive/robust boundary control can asymptotically stabilize the nonlinear string. Numerical simulation of the closed loop system demonstrates the effectiveness of the proposed control.

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 Impulsive Pinning Markovian Switching Stochastic Complex Networks with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Chen Xu ◽  
Jingyi Wang ◽  
Jianwen Feng ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Sufficient Conditions ◽  
Pinning Control ◽  
Functional Method ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Stochastic Complex Networks

The synchronization problem of stochastic complex networks with Markovian switching and time-varying delays is investigated by using impulsive pinning control scheme. The complex network possesses noise perturbations, Markovian switching, and internal and outer time-varying delays. Sufficient conditions for synchronization are obtained by employing the Lyapunov-Krasovskii functional method, Itö's formula, and the linear matrix inequality (LMI). Numerical examples are also given to demonstrate the validity of the theoretical results.

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