scholarly journals DII-Based Linear Feedback Control Design for Practical Synchronization of Chaotic Systems with Uncertain Input Nonlinearity and Application to Secure Communication

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Exponential Convergence ◽  
Chaotic Synchronization ◽  
Linear Control ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Input Nonlinearity ◽  
Uncertain Input

The concept of practical synchronization is introduced and the chaos synchronization of master-slave chaotic systems with uncertain input nonlinearities is investigated. Based on the differential and integral inequalities (DII) approach, a simple linear control is proposed to realize practical synchronization for master-slave chaotic systems with uncertain input nonlinearities. Besides, the guaranteed exponential convergence rate can be prespecified. Applications of proposed master-slave chaotic synchronization technique to secure communication as well as several numerical simulations are given to demonstrate the feasibility and effectiveness of the obtained result.

Robust finite-time chaos synchronization of time-delay chaotic systems and its application in secure communication

2016 ◽  
Vol 40 (4) ◽  
pp. 1177-1187 ◽  
Author(s):  
Hua Wang ◽  
Jian-Min Ye ◽  
Zhong–Hua Miao ◽  
Edmond A Jonckheere
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Finite Time ◽  
Secure Communication ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Chaotic Synchronization ◽  
Uncertain Parameters ◽  
Wide Range ◽  
Zero Items

This paper presents finite-time chaos synchronization of time-delay chaotic systems with uncertain parameters. According to the proposed method, a lot of coupled items can be treated as zero items. Thus, the whole system can be simplified greatly. Based on robust chaotic synchronization, secure communication can be realized with a wide range of parameter disturbance and time-delay. Numerical simulations are provided to illustrate the effectiveness of the proposed method.

Synchronization Controlling for the Chu Chaotic System via Linear Feedback

2011 ◽  
Vol 130-134 ◽  
pp. 2481-2484
Author(s):  
Ji Gui Jian ◽  
Xiao Lian Deng ◽  
Yan Jun Shen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Simple Structure ◽  
Matrix Theory ◽  
Exponential Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Inequality Techniques ◽  
Synchronization Scheme

Based on inequality techniques and matrix theory, linear feedback control both with one input and one state or two states and with multi-inputs is proposed to realize the globally exponential synchronization of two Chu chaotic systems. Some new sufficient algebraic criteria for the globally exponential synchronization of two chaotic systems are obtained analytically. The controllers here designed have simple structure. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

FREQUENCY-DOMAIN CRITERIA FOR GLOBAL SYNCHRONIZATION OF MULTISCROLL CHAOTIC SYSTEMS UNDER LINEAR FEEDBACK CONTROL

2010 ◽  
Vol 20 (07) ◽  
pp. 2165-2177 ◽  
Author(s):  
XIAOFENG WU ◽  
ZHIFANG GUI ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Frequency Domain ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
General Mathematical Model ◽  
Linear State ◽  
Absolute Stability Theory

This paper provides a unified approach for achieving and analyzing global synchronization of a class of master-slave coupled multiscroll chaotic systems under linear state-error feedback control. A general mathematical model for such a class of multiscroll chaotic systems is first established. Based on some special properties of such systems, two less-conservative frequency-domain criteria for the desirable global synchronization are rigorously proven by means of the absolute stability theory. The analysis is then applied to two master-slave coupled modified Chua's circuits, obtaining the corresponding simple and precise algebraic criteria for global synchronization, which are finally verified by numerical simulations.

Linear Control Root-Clustering of Uncertain Systems

2014 ◽  
Author(s):  
S. Gutman
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Linear Control ◽  
Linear Control Systems ◽  
Linear Feedback ◽  
Important Class ◽  
Linear Feedback Control ◽  
Control Root ◽  
Clustering Criterion

In the design of linear control systems, it is desired to assign the closed loop spectrum in sub-regions (as opposed to locations) of the complex plane. The present paper establishes a matrix root-clustering criterion for an important class of regions, and develops a linear feedback control that assigns the closed loop spectrum in the desired region. This is done for both nominal and uncertain systems.

Master-Slave Global Synchronization for Froude Pendulums via Linear State Error Feedback Control

2013 ◽  
Vol 275-277 ◽  
pp. 2565-2569
Author(s):  
Lin Xu ◽  
Zhong Liu ◽  
Yun Chen
Keyword(s):  
Feedback Control ◽  
Chaos Synchronization ◽  
Linear Feedback ◽  
Error Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Numerical Example ◽  
Linear State ◽  
Synchronization Scheme ◽  
State Error

This paper deals with the global chaos synchronization of master-slave Froude pendulums coupled by linear state error feedback control. A master-slave synchronization scheme of the Froude pendulums under linear feedback control is presented. Based on this scheme, some sufficient criteria for global synchronization are proved and optimized. A numerical example is provided to demonstrate the effectiveness of the criteria obtained.

THREE SCHEMES TO SYNCHRONIZE CHAOTIC FRACTIONAL-ORDER RUCKLIDGE SYSTEMS

2007 ◽  
Vol 21 (12) ◽  
pp. 2033-2044 ◽  
Author(s):  
YANBIN ZHANG ◽  
TIANSHOU ZHOU
Keyword(s):  
Dynamical Systems ◽  
Fractional Order ◽  
System Parameter ◽  
Chaotic Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Synchronization Problem ◽  
Alternate Choice ◽  
Parameter Values ◽  
Fractional Orders

The synchronization problem of chaotic fractional-order Rucklidge systems is studied both theoretically and numerically. Three different synchronization schemes based on the Pecora–Carroll principle, the linear feedback control and the bidirectional coupling are proposed to realize chaotic synchronization. It is shown that such schemes can achieve the same aim for the same set of system parameter values (including fractional orders). This provides an alternate choice for applications of fractional-order dynamical systems in engineering fields.

scholarly journals Chaotic Synchronization of Modified Discrete-Time Tinkerbell Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ke Ding ◽  
Xing Xu
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Discrete Time ◽  
Chaotic Synchronization ◽  
Linear Feedback ◽  
Linear Feedback Control

This paper studies chaotic synchronization of modified discrete-time Tinkerbell systems. By constructing the Lyapunov function and using the linear feedback control, some synchronization criteria for modified discrete-time Tinkerbell systems are derived. The conservativeness of those synchronization criteria is compared. The effectiveness of derived results is demonstrated by six examples.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

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