scholarly journals Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control

2011 ◽  
Vol 2 (1) ◽  
pp. 17-28
Author(s):  
Vaidyanathan SUNDARAPANDIAN ◽  
Karthikeyan RAJAGOPAL
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Uncertain Chaotic Systems

In this paper, we apply adaptive control method toderive new results for the anti-synchronization of identical Tigansystems (2008), identical Li systems (2009) and non-identical Tiganand Li systems. In adaptive anti-synchronization of identical chaoticsystems, the parameters of the master and slave systems are unknownand we devise feedback control law using the estimates of the systemparameters. In adaptive anti-synchronization of non-identical chaoticsystems, the parameters of the master system are known, but theparameters of the slave system are unknown and we devise feedbackcontrol law using the estimates of the parameters of the slave system.Our adaptive synchronization results derived in this paper for theuncertain Tigan and Li systems are established using Lyapunovstability theory. Since the Lyapunov exponents are not required forthese calculations, the adaptive control method is very effective andconvenient to achieve anti-synchronization of identical and nonidenticalTigan and Li systems. Numerical simulations are shown todemonstrate the effectiveness of the adaptive anti-synchronizationschemes for the uncertain chaotic systems addressed in this paper.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC AND CHAOTIC SYSTEMS BY ADAPTIVE CONTROL

2008 ◽  
Vol 18 (12) ◽  
pp. 3731-3736 ◽  
Author(s):  
ZHI-YU LIU ◽  
CHIA-JU LIU ◽  
MING-CHUNG HO ◽  
YAO-CHEN HUNG ◽  
TZU-FANG HSU ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Mean Squared Error ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Slave System ◽  
Unknown Parameters ◽  
Squared Error ◽  
Master System ◽  
Two Systems ◽  
The Mean

This paper presents the synchronization between uncertain hyperchaotic and chaotic systems. Based on Lyapunov stability theory, an adaptive controller is derived to achieve synchronization of hyperchaotic and chaotic systems, including the case of unknown parameters in these two systems. The T.N.Č. hyperchaotic oscillator is used as the master system, and the Rössler system is used as the slave system. Numerical simulations verify these results. Additionally, the effect of noise is investigated by measuring the mean squared error (MSE) of two systems.

H_Infinity Anti-Synchronization of Chaotic Systems with Unknown Parameters

2013 ◽  
Vol 336-338 ◽  
pp. 528-531 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Hui Zhang
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Chaotic Systems ◽  
External Disturbance ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Lyapunov Control ◽  
Norm Constraint ◽  
General Method

In this paper, a general method is proposed for the anti-synchronization of chaotic systems with unknown parameters. This approach is based on the Lyapunov control theory, and employs a combination of feedback control and adaptive control. With this method, the unknown parameters is estimated and the adaptive feedback controller is designed to not only guarantee stable anti-synchronization but also reduce the effect of external disturbance to an norm constraint. Numerical simulations results are presented to demonstrate the effectiveness of the method.

ADAPTIVE SYNCHRONIZATION FOR A CLASS OF HIGH-DIMENSIONAL AUTONOMOUS UNCERTAIN CHAOTIC SYSTEMS

2007 ◽  
Vol 18 (03) ◽  
pp. 399-406 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Chaotic Systems ◽  
Identification Problem ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
High Dimensional ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Uncertain Chaotic Systems ◽  
Unknown System

This paper addresses the adaptive synchronization and parameters identification problem of a class of high-dimensional autonomous uncertain chaotic systems. It is proved that the controller and update rule can make the states of the drive system and the response system with unknown system parameters asymptotically synchronized, and identify the response system's unknown parameters. Chen system, coupled dynamos system and Rössler hyperchaotic system are used as examples for detailed description. The results of numerical simulations show the effectiveness of the adaptive controller.

GENERALIZED (LAG, ANTICIPATED AND COMPLETE) PROJECTIVE SYNCHRONIZATION IN TWO NONIDENTICAL CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

2012 ◽  
Vol 26 (16) ◽  
pp. 1250121
Author(s):  
XINGYUAN WANG ◽  
LULU WANG ◽  
DA LIN
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Control Approach ◽  
Response System ◽  
Hyperchaotic Lorenz System

In this paper, a generalized (lag, anticipated and complete) projective synchronization for a general class of chaotic systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated and complete) projective synchronization between the drive system and response system based on the adaptive control method and feedback control approach. The hyperchaotic Chen system and hyperchaotic Lorenz system are chosen to illustrate the proposed scheme. Numerical simulations are provided to show the effectiveness of the proposed schemes. In addition, the scheme can also be extended to research generalized (lag, anticipated and complete) projective synchronization between nonidentical discrete-time chaotic systems.

ADAPTIVE ROBUST SYNCHRONIZATION FOR A CLASS OF DIFFERENT UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 22 (23) ◽  
pp. 4069-4082 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Chaotic Systems ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Robust Controller ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Predicted Values

This paper addresses the adaptive synchronization problem of a class of different uncertain chaotic systems. A general adaptive robust controller and parameters update rule are designed. It is proved theoretically that the controller and update rule can make the drive-response systems with different structures asymptotically synchronized, and change the unknown parameters to constants when noise exists. When the drive system is certain, the unknown parameters of the response system can be updated to the predicted values. The results of numerical simulations show the effectiveness of the adaptive controller.

Sign in / Sign up

Export Citation Format

Share Document