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.

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.

scholarly journals Comprehension and Thinking of Complex Network Construction and Clustering Based on Neural Network Algorithm

2018 ◽  
Vol 173 ◽  
pp. 03040
Author(s):  
Bing Shen
Keyword(s):  
Neural Network ◽  
Complex Networks ◽  
Complex Network ◽  
Small World ◽  
Network Clustering ◽  
Clustering Methods ◽  
Development History ◽  
Network Algorithm ◽  
Neural Network Algorithm ◽  
Application Fields

With the development of computer technology and the enhancement of people's cognition of the world, more and more scholars have been focusing on the research of complex networks. At the same time, the emerging machine learning neural network algorithm has become a powerful tool for various researchers. This paper mainly discusses the construction and clustering of complex networks based on neural network algorithm. Firstly, the development history and main application fields of neural network are introduced. Then, several common methods of complex network clustering are summarized, and then the limitations of these clustering methods are discussed. At last, it proposes to improve the construction of neural network through the concept of small world in complex network and enhance the effect of complex network clustering by the characteristics of neural network algorithm, including the accuracy, reliability, stability, speed, etc.

HYBRID PINNING CONTROL FOR COMPLEX NETWORKS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250252 ◽  
Author(s):  
LUIZ FELIPE R. TURCI ◽  
ELBERT E. N. MACAU
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Chaos Control ◽  
Dynamical Behavior ◽  
Pinning Control ◽  
Synchronization Control ◽  
Network Nodes

In this work, we present two different hybrid pinning strategies to synchronize a complex network of identical agents into a known desired solution. The first strategy is the chaos control hybrid pinning in which pinning synchronization control and chaos control are merged. The second strategy is the nonidentical reference hybrid pinning, in which the pinning reference dynamical behavior is different from network nodes dynamical behavior.

Synchronization of time-varying coupled complex networks via adaptive pinning control

2021 ◽  
pp. 2150164
Author(s):  
Hai Lin ◽  
Jincheng Wang
Keyword(s):  
Lyapunov Function ◽  
Complex Networks ◽  
Complex Network ◽  
Function Theory ◽  
Pinning Control ◽  
Time Varying ◽  
Control Parameters ◽  
State Variables ◽  
Network Time ◽  
Adaptive Coupling

Pinning synchronization of complex networks with two different kinds of time-varying coupling are studied in this paper. Inner coupling of the state variables and outer coupling in the complex network are taken into consideration. Based on the Lyapunov function theory, some general criteria and a simplified corollary for ensuring network synchronization are proposed. Linear pinning controllers, adaptive pinning controllers and adaptive coupling strength are designed for achieving complex network time-varying synchronization. Furthermore, the analytic relationship between control parameters is studied. Numerical simulations further illustrate the effectiveness of conclusions.

THE LOCAL STOCHASTIC STABILITY FOR COMPLEX NETWORKS UNDER PINNING CONTROL

2012 ◽  
Vol 22 (05) ◽  
pp. 1250113 ◽  
Author(s):  
ZHOU YAN ◽  
XIAO-LING JIN ◽  
ZHI-LONG HUANG
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Stochastic Stability ◽  
Pinning Control ◽  
Damping Coefficient ◽  
Largest Lyapunov Exponent ◽  
Stochastic Perturbations ◽  
The Matrix ◽  
Negative Damping ◽  
System Of Parameters

The local stochastic stability of complex networks under pinning control is studied, with stochastic perturbations to the coupling strengths. The nodes of complex network are modeled as second-order differential equations subject to stochastic parametric excitations. The complex network is first linearized at its trivial solution, and the resulting equations are reduced to independent subsystems by using a suitable linear transformation. Then the condition of the stochastic stability can be determined by Lyapunov exponents of the subsystems. The largest Lyapunov exponent of the subsystem can be expressed analytically, as a function of the eigenvalue of a matrix associated with the coupling matrix and pinning control matrix for a given system of parameters. And the stability region with respect to the eigenvalue can be obtained. It is pointed out that the local stochastic stability of the network is finally determined by the maximal and minimum eigenvalues of the matrix. Numerical results with positive and negative damping coefficients are given to illustrate the criterion. Moreover, for the positive damping coefficient case, the pinning control may destabilize the network; and for the negative damping coefficient case, the pinning control may stabilize the network.

ON SYNCHRONIZATION OF DISCRETE-TIME MARKOVIAN JUMPING STOCHASTIC COMPLEX NETWORKS WITH MODE-DEPENDENT MIXED TIME-DELAYS

2009 ◽  
Vol 23 (03) ◽  
pp. 411-434 ◽  
Author(s):  
YURONG LIU ◽  
ZIDONG WANG ◽  
XIAOHUI LIU
Keyword(s):  
Complex Networks ◽  
Complex Network ◽  
Discrete Time ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Disturbances ◽  
Coupling Term ◽  
Markovian Jumping

In this paper, the synchronization problem is investigated for a new class of discrete-time complex networks. Such complex networks involve the Markovian jumping parameters, mode-dependent discrete and distributed time-delays, constant and delayed couplings, as well as multiple stochastic disturbances. The stochastic disturbances influence the constant coupling term, the delayed coupling term, as well as the overall network dynamics, which could better describe the dynamical behavior of a coupled complex network presented within a noisy environment. With help from the Lyapunov functional method and the properties of Kronecker product, we employ the stochastic analysis techniques to derive several delay-dependent sufficient conditions under which the coupled complex network is asymptotically synchronized in the mean square. The criteria obtained in this paper are in the form of LMIs whose solution can be easily calculated using the standard numerical software. It is shown that our main results can cover many existing ones reported in the literature. A numerical example is presented to illustrate the usefulness of our results.

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