Adaptive controller design for lag-synchronization of two non-identical time-delayed chaotic systems with unknown parameters

2011 ◽  
Vol 375 (17) ◽  
pp. 1769-1778 ◽  
Author(s):  
Shabnam Pourdehi ◽  
Paknosh Karimaghaee ◽  
Dena Karimipour
Keyword(s):  
Chaotic Systems ◽  
Controller Design ◽  
Adaptive Controller ◽  
Unknown Parameters ◽  
Lag Synchronization

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

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.

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.

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.

GENERALIZED SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS BASED ON PARAMETER IDENTIFICATION

2009 ◽  
Vol 23 (22) ◽  
pp. 2593-2606 ◽  
Author(s):  
YONGGUANG YU ◽  
HAN-XIONG LI ◽  
JUNZHI YU
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Generalized Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Response System ◽  
Generalized Lorenz System ◽  
The One

This paper investigates the generalized synchronization issue for two different dimensional chaotic systems with unknown parameters. Based on Lyapunov stability theory and adaptive control theory, an adaptive controller is derived to achieve the generalized synchronization whether the dimension of drive system is greater than the one of the response system or not. Meanwhile, corresponding parameter updating laws can be obtained so as to exactly identify uncertain parameters. This technique has been successfully applied to two examples, the generalized synchronization of hyperchaotic Rössler system and chaotic Lorenz system, chaotic Chen system and generalized Lorenz system. Numerical simulations are finally shown to illustrate the effectiveness of the proposed approach.

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hadi Delavari ◽  
Milad Mohadeszadeh
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Robust Adaptive ◽  
Complex Chaotic Systems

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

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