scholarly journals ROBUST SYNCHRONIZATION WITH UNIFORM ULTIMATE BOUND BETWEEN TWO DIFFERENT CHAOTIC SYSTEMS WITH UNCERTAINTIES

2011 ◽  
Vol 25 (16) ◽  
pp. 2217-2227
Author(s):  
JIANPING CAI ◽  
ZHENGZHONG YUAN
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Chen System ◽  
Adaptive Controllers ◽  
External Perturbations ◽  
Response Systems ◽  
The Lorenz System ◽  
Different Chaotic Systems ◽  
Ultimate Bound

Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions the drive-response systems can achieve synchronization with uniform ultimate bound even though the bounds of uncertainties are not known exactly in advance. The designed controllers contain only feedback terms and partial nonlinear terms of the systems, and they are easy to implement in practice. The Lorenz system and Chen system are chosen as the illustrative example to verify the validity of the proposed method. Simulation results also show that the present control has good robustness against different kinds of disturbances.

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.

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.

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

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.

scholarly journals Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. M. El-Dessoky ◽  
M. T. Yassen ◽  
E. Saleh
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Chen System ◽  
Adaptive Controllers ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Modified Function Projective Synchronization ◽  
Hyperchaotic Lorenz System

This work investigates modified function projective synchronization between two different hyperchaotic dynamical systems, namely, hyperchaotic Lorenz system and hyperchaotic Chen system with fully unknown parameters. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between two diffierent hyperchaotic dynamical systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE IDENTICAL AND DIFFERENT CYQY HYPER-CHAOTIC SYSTEMS

2014 ◽  
Vol 28 (04) ◽  
pp. 1450013 ◽  
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
NA WEI ◽  
SI-HUI JIANG ◽  
XIU-KUN WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper further investigates the adaptive full state hybrid projective synchronization (FSHPS) of hyper-chaotic systems — CYQY system with fully unknown parameters and perturbations. Based on the Lyapunov stability theory, adaptive controllers and updating laws of parameters can be designed for achieving the FSHPS of the CYQY hyper-chaotic systems with the same and different structures. Two groups numerical simulations are provided to verify the effectiveness of the proposed scheme.

ADAPTIVE GENERALIZED SYNCHRONIZATION OF HYPERCHAOS SYSTEMS

2011 ◽  
Vol 25 (32) ◽  
pp. 4563-4571 ◽  
Author(s):  
XINGYUAN WANG ◽  
YAQIN WANG
Keyword(s):  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
New Method ◽  
Generalized Synchronization ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lorenz System ◽  
Linear And Nonlinear ◽  
Simulation Results

This paper studies the generalized synchronization of hyperchaos systems, and a new method, by which adaptive generalized synchronization of chaotic systems with a kind of linear and nonlinear relationship between the drive and response systems can be achieved, is proposed. This new method has more extensive application scope. Based on the Lyapunov stability theory, the correctness of the proposed scheme is strictly demonstrated. It is also illustrated by applications to hyperchaotic Chen system and hyperchaotic Lorenz system and the simulation results show the effectiveness of the proposed scheme.

scholarly journals Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiuchun Li ◽  
Jianhua Gu ◽  
Wei Xu
Keyword(s):  
Neural Network ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Original System ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
External Perturbations ◽  
Response Systems ◽  
Barbalat Lemma

Considering the effects of external perturbations on the state vector and the output of the original system, this paper proposes a new adaptive integral observer method to deal with chaos synchronization between the drive and response systems with unknown parameters. The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constraints because many parameters related to chaotic system can be unknown, as shown in the paper. Numerical simulations are performed in the end and the results show that the proposed method is not only suitable to the representative chaotic systems but also applied to some neural network chaotic systems.

scholarly journals Adaptive Anti-synchronization of Identical and Non-identical 4-D Chaotic Systems

2012 ◽  
pp. 160-164
Author(s):  
H. Najafizadegan ◽  
M. Khoeiniha ◽  
H. Zarabadipour
Keyword(s):  
Adaptive Control ◽  
Theoretical Analysis ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Unknown Parameters ◽  
Different Chaotic Systems ◽  
Adaptive Control Law

In this paper, we investigate the chaos anti-synchronization between two identical and different chaotic systems with fully unknown parameters via adaptive control. Based on the Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are designed such that the two different chaotic systems can be anti-synchronized asymptotically. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals Robust Adaptive Finite-Time Synchronization of Two Different Chaotic Systems with Parameter Uncertainties

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yun-An Hu ◽  
Hai-Yan Li ◽  
Chun-Ping Zhang ◽  
Liang Liu
Keyword(s):  
Finite Time ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Parameter Uncertainties ◽  
Unknown Parameters ◽  
Control Approach ◽  
Different Chaotic Systems

This paper is concerned with the finite-time synchronization problem for two different chaotic systems with parameter uncertainties. Using finite-time control approach and robust control method, an adaptive synchronization scheme is proposed to make the synchronization errors of the systems with parameter uncertainties zero in a finite time. On the basis of Lyapunov stability theory, appropriate adaptive laws are derived to deal with the unknown parameters of the systems. And the convergence of the parameter errors is guaranteed in a finite time. The proposed method can be applied to a variety of chaos systems. Numerical simulations are given to demonstrate the efficiency of the proposed control scheme.

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