Anticipating Synchronization of Chaotic Systems with Parameter Mismatch

2008 ◽  
Author(s):  
Qi Han ◽  
Chuandong Li ◽  
Junjian Huang ◽  
Xiaofeng Liao ◽  
Tingwen Huang
Keyword(s):  
Chaotic Systems ◽  
Parameter Mismatch

ADAPTIVE OBSERVER BASED SYNCHRONIZATION OF A CLASS OF UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (08) ◽  
pp. 2425-2435 ◽  
Author(s):  
SAMUEL BOWONG ◽  
RENÉ YAMAPI
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Observer ◽  
Adaptive Synchronization ◽  
External Disturbances ◽  
Parameter Mismatch ◽  
Lipschitz Constants ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Robust Adaptive

This study addresses the adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. For a class of uncertain chaotic systems with parameter mismatch and external disturbances, a robust adaptive observer based on the response system is constructed to practically synchronize the uncertain drive chaotic system. Lyapunov stability theory ensures the practical synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of two illustrative examples are given to verify the effectiveness of the proposed method.

scholarly journals SYNCHRONIZATION OF A CLASS OF MASTER–SLAVE NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA SINUSOIDAL FEEDBACK CONTROL

2011 ◽  
Vol 25 (16) ◽  
pp. 2195-2215 ◽  
Author(s):  
JIANPING CAI ◽  
MIHUA MA ◽  
XIAOFENG WU
Keyword(s):  
Feedback Control ◽  
Error Bound ◽  
Error Bounds ◽  
Chaotic Systems ◽  
Direct Method ◽  
Harmonic Excitation ◽  
Synchronization Error ◽  
Error Feedback ◽  
Parameter Mismatch ◽  
State Error

In this paper, we investigate a master–slave synchronization scheme of two n-dimensional nonautonomous chaotic systems coupled by sinusoidal state error feedback control, where parameter mismatch exists between the external harmonic excitation of master system and that of slave one. A concept of synchronization with error bound is introduced due to parameter mismatch, and then the bounds of synchronization error are estimated analytically. Some synchronization criteria are firstly obtained in the form of matrix inequalities by the Lyapunov direct method, and then simplified into some algebraic inequalities by the Gerschgorin disc theorem. The relationship between the estimated synchronization error bound and system parameters reveals that the synchronization error can be controlled as small as possible by increasing the coupling strength or decreasing the magnitude of mismatch. A three-dimensional gyrostat system is chosen as an example to verify the effectiveness of these criteria, and the estimated synchronization error bounds are compared with the numerical error bounds. Both the theoretical and numerical results show that the present sinusoidal state error feedback control is effective for the synchronization. Numerical examples verify that the present control is robust against amplitude or phase mismatch.

SYNCHRONIZING CHAOS BY IMPULSIVE FEEDBACK METHOD

2001 ◽  
Vol 11 (08) ◽  
pp. 2233-2243 ◽  
Author(s):  
Y. ZHANG ◽  
G. H. DU ◽  
J. J. JIANG
Keyword(s):  
Frequency Spectrum ◽  
Potential Application ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Chaotic Communication ◽  
Parameter Mismatch ◽  
Practical Experiment ◽  
Chaotic Solution ◽  
Robustness To Noise ◽  
Feedback Method

In this letter, the impulsive feedback synchronization method is suggested. Synchronization condition is given by investigating the mechanism of the impulsive feedback synchronization. Furthermore, we consider the influences of noise and parameter mismatch since they inevitably exist in the practical experiment. Finally, a visual circuit implementation of impulsive feedback synchronization is performed. The research demonstrates that impulsive operator can spread frequency spectrum of chaotic solution. Impulsive feedback can synchronize chaotic systems and has the robustness to noise and parameter mismatch. It shows the potential application in chaotic communication.

scholarly journals On the Synchronization of Chaos Systems by Using State Observers

1997 ◽  
Vol 07 (06) ◽  
pp. 1307-1322 ◽  
Author(s):  
Ömer Morgül ◽  
Ercan Solak
Keyword(s):  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Observer Design ◽  
Global Synchronization ◽  
Parameter Mismatch ◽  
Mild Conditions ◽  
Chua’S Oscillator ◽  
State Observers ◽  
Local Synchronization ◽  
Synchronization Scheme

We show that the synchronization of chaotic systems can be achieved by using the observer design techniques which are widely used in the control of dynamical systems. We prove that local synchronization is possible under relatively mild conditions and global synchronization is possible if the chaotic system has some special structures, or can be transformed into some special forms. We show that some existing synchronization schemes for chaotic systems are related to the proposed observer-based synchronization scheme. We prove that the proposed scheme is robust with respect to noise and parameter mismatch under some mild conditions. We also give some examples including the Lorenz and Rössler systems and Chua's oscillator which are known to exhibit chaotic behavior, and show that in these systems synchronization by using observers is possible.

Output Tracking Control and Synchronization of Continuous Chaotic Systems Using Differential Evolution Algorithm

2010 ◽  
Vol 37-38 ◽  
pp. 823-828
Author(s):  
Shu Bo Liu ◽  
Shu Min Zhou ◽  
Li Yong Hu
Keyword(s):  
Differential Evolution ◽  
Tracking Control ◽  
Chaotic Systems ◽  
Differential Evolution Algorithm ◽  
Theoretical Method ◽  
Parameter Mismatch ◽  
Single Input Single Output ◽  
Output Tracking ◽  
Output Tracking Control ◽  
Control And Synchronization

This paper applies differential evolution (DE) algorithm to realize the output tracking control and synchronization of continuous chaotic systems. The output tracking control of single-input single-output (SISO) and multi-input multi-output (MIMO) chaotic system is investigated. Moreover, synchronization of chaotic systems with parameter mismatch or structure difference is also under discussion. Numerical simulations based on the well-known models such as Lorenz and Chen systems are used to illustrate the validity of this theoretical method.

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