scholarly journals Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

Entropy ◽  
2013 ◽  
Vol 16 (1) ◽  
pp. 377-388 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Projective Synchronization ◽  
Generalized Function ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Hyperchaotic Systems ◽  
Generalized Function Projective Synchronization

Complete Switched Generalized Function Projective Synchronization of a Class of Hyperchaotic Systems With Unknown Parameters and Disturbance Inputs

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Fei Yu ◽  
Yun Song
Keyword(s):  
Numerical Simulations ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Generalized Function ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Hyperchaotic Systems ◽  
Generalized Function Projective Synchronization

The concept of complete switched generalized function projective synchronization (CSGFPS) in practical type is introduced and the CSGFPS of a class of hyperchaotic systems with unknown parameters and disturbance inputs are investigated. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the states of a class of hyperchaotic systems asymptotically synchronized up to a desired scaling function and the unknown parameters are also estimated. In numerical simulations, the scaling function factors discussed in this paper are more complicated. Finally, the hyperchaotic Lorenz and hyperchaotic Lü systems are taken, for example, and the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

scholarly journals A New 4D Hyperchaotic System and Its Generalized Function Projective Synchronization

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yuan Gao ◽  
Chenghua Liang
Keyword(s):  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Generalized Function ◽  
Hyperchaotic System ◽  
Function Projective Synchronization ◽  
And Function ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Generalized Function Projective Synchronization ◽  
New System

A new four-dimensional hyperchaotic system is investigated. Numerical and analytical studies are carried out on its basic dynamical properties, such as equilibrium point, Lyapunov exponents, Poincaré maps, and chaotic dynamical behaviors. We verify the realizability of the new system via an electronic circuit by using Multisim software. Furthermore, a generalized function projective synchronization scheme of two different hyperchaotic systems with uncertain parameters is proposed, which includes some existing projective synchronization schemes, such as generalized projection synchronization and function projective synchronization. Based on the Lyapunov stability theory, a controller with parameters update laws is designed to realize synchronization. Using this controller, we realize the synchronization between Chen hyperchaotic system and the new system to verify the validity and feasibility of our method.

scholarly journals Robust Adaptive Sliding Mode Control for Generalized Function Projective Synchronization of Different Chaotic Systems with Unknown Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiuchun Li ◽  
Jianhua Gu ◽  
Wei Xu
Keyword(s):  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Generalized Function ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode ◽  
Function Projective Synchronization ◽  
Response Systems ◽  
Generalized Function Projective Synchronization

When the parameters of both drive and response systems are all unknown, an adaptive sliding mode controller, strongly robust to exotic perturbations, is designed for realizing generalized function projective synchronization. Sliding mode surface is given and the controlled system is asymptotically stable on this surface with the passage of time. Based on the adaptation laws and Lyapunov stability theory, an adaptive sliding controller is designed to ensure the occurrence of the sliding motion. Finally, numerical simulations are presented to verify the effectiveness and robustness of the proposed method even when both drive and response systems are perturbed with external disturbances.

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