scholarly journals Exponential Synchronization Analysis and Control for Discrete-Time Uncertain Delay Complex Networks with Stochastic Effects

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Tianbo Wang ◽  
Wuneng Zhou ◽  
Dejun Zhao ◽  
Shouwei Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Control Methods ◽  
Stochastic Effects ◽  
Inequality Technique ◽  
The Difference ◽  
And Control

The exponential synchronization for a class of discrete-time uncertain complex networks with stochastic effects and time delay is investigated by using the Lyapunov stability theory and discrete Halanay inequality. The uncertainty arises from the difference of the nodes’ reliability in the complex network. Through constructing an appropriate Lyapunov function and applying inequality technique, some synchronization criteria and two control methods are obtained to ensure the considered complex network being exponential synchronization. Finally, a numerical example is provided to show the effectiveness of our proposed methods.

Function Projective Synchronization in Complex Networks with Stochastic Effects via Hybrid Feedback Control

2014 ◽  
Vol 511-512 ◽  
pp. 1008-1011
Author(s):  
Yun Guo Jin ◽  
Shou Ming Zhong
Keyword(s):  
Feedback Control ◽  
Complex Networks ◽  
Control Method ◽  
Exponential Synchronization ◽  
Projective Synchronization ◽  
Mean Square ◽  
Stochastic Effects ◽  
Function Projective Synchronization ◽  
Feedback Control Method

In this paper, the problem of function projective synchronization is investigated for complex networks with stochastic effects. A hybrid feedback control method is designed to achieve function projective synchronization for the complex networks. Using Gronwally' inequality, we obtain some conditions to guarantee that the complex networks can realize mean square synchronization and mean square exponential synchronization, respectively.

On the Proper Description of Complex Network Dynamics

2018 ◽  
Author(s):  
Chun-Lin Yang ◽  
C. Steve Suh
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Collective Behavior ◽  
Local Level ◽  
Network Dynamics ◽  
Global Dynamics ◽  
Statistical Entropy ◽  
Network Systems ◽  
Local Dynamics ◽  
The Difference

Real-world networks are dynamical complex network systems. The dynamics of a network system is a coupling of the local dynamics with the global dynamics. The local dynamics is the time-varying behaviors of ensembles at the local level. The global dynamics is the collective behavior of the ensembles following specific laws at the global level. These laws include basic physical principles and constraints. Complex networks have inherent resilience that offsets disturbance and maintains the state of the system. However, when disturbance is potent enough, network dynamics can be perturbed to a level that ensembles no longer follow the constraint conditions. As a result, the collective behavior of a complex network diminishes and the network collapses. The characteristic of a complex network is the response of the system which is time-dependent. Therefore, complex networks need to account for time-dependency and obey physical laws and constraints. Statistical mechanics is viable for the study of multi-body dynamic systems having uncertain states such as complex network systems. Statistical entropy can be used to define the distribution of the states of ensembles. The difference between the states of ensembles define the interaction between them. This interaction is known as the collective behavior. In other words statistical entropy defines the dynamics of a complex network. Variation of entropy corresponds to the variation of network dynamics and vice versa. Therefore, entropy can serve as an indicator of network dynamics. A stable network is characterized by a specific entropy while a network on the verge of collapse is characterized by another. As the collective behavior of a complex network can be described by entropy, the correlation between the statistical entropy and network dynamics is investigated.

scholarly journals Controllability and Optimization of Complex Networks Based on Bridges

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lifu Wang ◽  
Guotao Zhao ◽  
Zhi Kong ◽  
Yunkang Zhao
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Betweenness Centrality ◽  
The Other ◽  
Connected Components ◽  
Scale Free ◽  
Scale Free Networks ◽  
Model Networks ◽  
Simulation Results ◽  
And Control

In a complex network, each edge has different functions on controllability of the whole network. A network may be out of control due to failure or attack of some specific edges. Bridges are a kind of key edges whose removal will disconnect a network and increase connected components. Here, we investigate the effects of removing bridges on controllability of network. Various strategies, including random deletion of edges, deletion based on betweenness centrality, and deletion based on degree of source or target nodes, are used to compare with the effect of removing bridges. It is found that the removing bridges strategy is more efficient on reducing controllability than the other strategies of removing edges for ER networks and scale-free networks. In addition, we also found the controllability robustness under edge attack is related to the average degree of complex networks. Therefore, we propose two optimization strategies based on bridges to improve the controllability robustness of complex networks against attacks. The effectiveness of the proposed strategies is demonstrated by simulation results of some model networks. These results are helpful for people to understand and control spreading processes of epidemic across different paths.

scholarly journals Outer Synchronization between Complex Networks with Nonlinear Time-Delay Characteristics and Time-Varying Topological Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xinli Fang ◽  
Qiang Yang ◽  
Wenjun Yan
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Lyapunov Stability Theory ◽  
Time Varying ◽  
Outer Synchronization ◽  
Topological Structures ◽  
Synchronization Problem ◽  
Adaptive Control Strategy ◽  
And Control ◽  
Time Invariant

This paper exploits the network outer synchronization problem in a generic context for complex networks with nonlinear time-delay characteristics and nonidentical time-varying topological structures. Based on the classic Lyapunov stability theory, the synchronization criteria and adaptive control strategy are presented, respectively, by adopting an appropriate Lyapunov-Krasovskii energy function and the convergence of the system error can also be well proved. The existing results of network outer synchronization can be obtained by giving certain conditions, for example, treating the coupling matrices as time-invariant, and by applying the suggested generic synchronization criteria and control scheme. The numerical simulation experiments for networks scenarios with dynamic chaotic characteristics and time-varying topologies are carried out and the result verifies the correctness and effectiveness of the proposed control solution.

Exponential synchronization of stochastic delayed discrete-time complex networks

2007 ◽  
Vol 53 (1-2) ◽  
pp. 153-165 ◽  
Author(s):  
Jinling Liang ◽  
Zidong Wang ◽  
Xiaohui Liu
Keyword(s):  
Complex Networks ◽  
Discrete Time ◽  
Exponential Synchronization

Design of a robust H∞ preview controller for a class of uncertain discrete-time systems

2017 ◽  
Vol 40 (8) ◽  
pp. 2639-2650 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Interference Rejection ◽  
Discrete Time Systems ◽  
Controller Gain ◽  
Error System ◽  
The Difference ◽  
System States ◽  
Time Systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

A Locally Exponential Synchronization Criterion for Complex Networks

2013 ◽  
Vol 380-384 ◽  
pp. 2415-2418
Author(s):  
Li Fu Wang ◽  
Peng Xue
Keyword(s):  
Complex Networks ◽  
Dimensional Space ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Two Dimensional ◽  
Fast Switching ◽  
Synchronization Problem ◽  
Error System ◽  
Lorenz Chaotic System ◽  
New Criterion

The exponential synchronization problem of complex networks is investigated. The complex network model considered is a moving agent network in a two dimensional space and the coupling of between nodes is nonlinear links. In order to achieve the objective of exponential synchronizaiton, linearizing error system is presented. Base on the Lyapunov stability theory, a new criterion is proposed for exponetial synchronization of moving agnets networks under the condition of fast switching. In addition, an numerical example of the Lorenz chaotic system are analyzed, and numerical simulations results show the effectiveness of proposed exponential synchronization criterion.

scholarly journals Exponential Synchronization of Two Nonlinearly Coupled Complex Networks with Time-Varying Delayed Dynamical Nodes

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Shao
Keyword(s):  
Complex Networks ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Time Varying Delay ◽  
Coupled Networks ◽  
Synchronization Scheme ◽  
Varying Delay

This paper investigates the exponential synchronization between two nonlinearly coupled complex networks with time-varying delay dynamical nodes. Based on the Lyapunov stability theory, some criteria for the exponential synchronization are derived with adaptive control method. Moreover, the presented results here can also be applied to complex dynamical networks with single time delay case. Finally, numerical analysis and simulations for two nonlinearly coupled networks which are composed of the time-delayed Lorenz chaotic systems are given to demonstrate the effectiveness and feasibility of the proposed complex network synchronization scheme.

scholarly journals Learning Impulsive Pinning Control of Complex Networks

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2436
Author(s):  
Alma Y. Alanis ◽  
Daniel Ríos-Rivera ◽  
Edgar N. Sanchez ◽  
Oscar D. Sanchez
Keyword(s):  
Neural Network ◽  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Pinning Control ◽  
Rayleigh Quotient ◽  
Control Input ◽  
Linear Connections ◽  
Algebra Approach ◽  
Unknown Node

In this paper, we present an impulsive pinning control algorithm for discrete-time complex networks with different node dynamics, using a linear algebra approach and a neural network as an identifier, to synthesize a learning control law. The model of the complex network used in the analysis has unknown node self-dynamics, linear connections between nodes, where the impulsive dynamics add feedback control input only to the pinned nodes. The proposed controller consists of the linearization for the node dynamics and a reorder of the resulting quadratic Lyapunov function using the Rayleigh quotient. The learning part of the control is done with a discrete-time recurrent high order neural network used for identification of the pinned nodes, which is trained using an extended Kalman filter algorithm. A numerical simulation is included in order to illustrate the behavior of the system under the developed controller. For this simulation, a 20-node complex network with 5 different node dynamics is used. The node dynamics consists of discretized versions of well-known continuous chaotic attractors.

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