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.

Globally Exponential Synchronization for the Genesio-Tesi Chaotic System via Feedback Control with Two States

2012 ◽  
Vol 229-231 ◽  
pp. 2298-2301
Author(s):  
Jiang Hong Guo ◽  
Ji Gui Jian
Keyword(s):  
Feedback Control ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Simple Structure ◽  
Matrix Theory ◽  
Exponential Synchronization ◽  
Inequality Techniques ◽  
Synchronization Scheme

Based on matrix theory and inequality techniques, feedback control with two states is proposed to realize the globally exponential synchronization of two Genesi-Tesi 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.

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.

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.

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.

GLOBAL SYNCHRONIZATION OF MULTI-SCROLL SATURATED CHAOTIC SYSTEMS VIA SINGLE-STATE LINEAR FEEDBACK CONTROL

2013 ◽  
Vol 27 (05) ◽  
pp. 1350007 ◽  
Author(s):  
ZHIFANG GUI ◽  
XIAOFENG WU ◽  
YUN CHEN
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Global Synchronization ◽  
Algebraic Criterion ◽  
Synchronization Problem ◽  
Single State ◽  
Conservative Result ◽  
Absolute Stability Theory

This paper investigates the global synchronization problem of master–slave coupled multi-scroll saturated chaotic systems via single-state linear feedback control. An algebraic criterion for global synchronization is rigorously proven by means of the absolute stability theory. The obtained algebraic criterion is then optimized thereby deriving a less-conservative result, which is finally verified by numerical examples.

scholarly journals SYNCHRONIZATION ERRORS AND UNIFORM SYNCHRONIZATION WITH AN ERROR BOUND FOR CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (11) ◽  
pp. 3341-3354 ◽  
Author(s):  
BIN LIU ◽  
DAVID J. HILL ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Theoretical Analysis ◽  
Error Bound ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Small Error ◽  
Channel Noise ◽  
Synchronization Errors ◽  
Synchronization Scheme

This paper investigates the problem of estimating synchronization errors and its application to uniform synchronization with an error bound for the general master-slave chaos synchronization scheme via feedback control, which is subjected to disturbances by unknown but bounded channel noise. Based on the Lyapunov function and nonlinear parametric variation techniques, estimation formulae for synchronization errors are derived. It is possible to synchronize two master-slave chaotic systems with a relatively small error bound, even in the case with unknown but bounded noisy disturbances. After the theoretical analysis, some representative examples and their numerical simulations are given for illustration.

Optimal Linear and Nonlinear Control Design for Chaotic Systems

2005 ◽  
Author(s):  
Marat Rafikov ◽  
Jose´ Manoel Balthazar
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Control Design ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Linear And Nonlinear

In this work, the linear and nonlinear feedback control techniques for chaotic systems were been considered. The optimal nonlinear control design problem has been resolved by using Dynamic Programming that reduced this problem to a solution of the Hamilton-Jacobi-Bellman equation. In present work the linear feedback control problem has been reformulated under optimal control theory viewpoint. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations for the Ro¨ssler system and the Duffing oscillator are provided to show the effectiveness of this method.

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