Generalized Projective Synchronization of a Novel Hyperchaotic Four-Wing System via Adaptive Control Method

2016 ◽  
pp. 275-296 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Ahmad Taher Azar
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Projective Synchronization ◽  
Generalized Projective Synchronization

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.

GENERALIZED PROJECTIVE SYNCHRONIZATION AND PARAMETERS ESTIMATION OF TWO NEW HYPERCHAOTIC SYSTEMS WITH FULLY UNCERTAIN PARAMETERS

2010 ◽  
Vol 21 (02) ◽  
pp. 249-259 ◽  
Author(s):  
CONG-XU ZHU
Keyword(s):  
Adaptive Control ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Parameters Estimation ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems ◽  
Theoretical Results

This paper investigates adaptive generalized projective synchronization (GPS) between two novel hyperchaotic systems with different structure and fully uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, GPS between the two hyperchaotic systems is achieved by proposing a new adaptive controller and a novel parameters estimation update law. Strict theoretical proof is put forward. Numerical simulations are presented to demonstrate the effectiveness of the proposed GPS scheme and verify the theoretical results.

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