Projective synchronization of time-delayed chaotic systems with unknown parameters using adaptive control method

2014 ◽  
Vol 38 (4) ◽  
pp. 726-737 ◽  
Author(s):  
Sana Parveen Ansari ◽  
Subir Das
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Projective Synchronization ◽  
Unknown Parameters

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.

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.

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 Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

2020 ◽  
Vol 9 (3) ◽  
pp. 597-611
Author(s):  
Ayub Khan ◽  
Harindri Chaudhary
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Chaos Control ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

Abstract In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

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