Adaptive Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2009 ◽  
Author(s):  
Jiang-Wen Xiao ◽  
Ning Qin ◽  
Yuehua Huang ◽  
Yan-Wu Wang
Keyword(s):  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Hyperchaotic Systems

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

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.

scholarly journals Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Meng ◽  
Xiaohong Wang
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Sliding Mode ◽  
Small Region ◽  
Hopfield Neural Networks ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Lyapunov Stability Criterion ◽  
Order Extension

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

2017 ◽  
Vol 6 (4) ◽  
pp. 1-16 ◽  
Author(s):  
A. Almatroud Othman ◽  
M.S.M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic 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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