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.

Switched Projective Synchronization of the Stochastic Newton-Leipnik System

2013 ◽  
Vol 328 ◽  
pp. 570-574
Author(s):  
Duan Dong ◽  
Shao Juan Ma ◽  
Jie Zheng
Keyword(s):  
Hilbert Spaces ◽  
Chaotic Systems ◽  
Control Method ◽  
Random Parameter ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Deterministic System ◽  
Lyapunov Stability Theorem ◽  
Orthogonal Polynomial Expansion

The paper is involved with switched projective synchronization of two identical chaotic systems with random parameter using adaptive control method. Based on the orthogonal polynomial expansion of the Hilbert spaces, the Newton-Leipnik system with random parameter is transformed as the equivalent deterministic system. At last, an adaptive controller can be designed by the Lyapunov stability theorem for achieving switched projective synchronization of the equivalent deterministic system with different initial values. Corresponding numerical simulations are performed to verify the effectiveness of presented schemes for synchronizing the stochastic Newton-Leipnik system.

scholarly journals Model Reference Control of Hyperchaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Pengfei Zhao ◽  
Cai Liu ◽  
Xuan Feng
Keyword(s):  
Lyapunov Stability ◽  
Reference System ◽  
Stability Theorem ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
General Description ◽  
Lyapunov Stability Theorem ◽  
Model Reference ◽  
Model Reference Control ◽  
Hyperchaotic Systems

We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for controlling hyperchaotic systems with both certain parameters and uncertain parameters.

ADAPTIVE SYNCHRONIZATION OF UNCERTAIN RÖSSLER SYSTEM BASED ON PARAMETER IDENTIFICATION

2008 ◽  
Vol 22 (23) ◽  
pp. 3987-3995 ◽  
Author(s):  
XINGYUAN WANG ◽  
XINGUANG LI
Keyword(s):  
Parameter Identification ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Stability Theorem ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Rossler System ◽  
Master System ◽  
Rössler System

Assuming the Rössler system as a reference, this paper studies two cases of chaotic synchronization of a pair of (master and slave) systems: one with fully uncertain parameters for both, the other where the master system has fixed given parameters while the slave system is endowed with uncertain parameters. The respective adaptive controller based on parameter identification is then designed, according to the Lyapunov stability theorem. Then, it is proved that the two controllers are capable of making the two (identical) Rössler systems asymptotically synchronized. Numerical simulation results further testify the efficiency of controllers.

Function projective synchronization of two four-scroll hyperchaotic systems with unknown parameters

Open Physics ◽  
2013 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhenwu Sun
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
System Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Hyperchaotic Systems

AbstractFunction projective synchronization (FPS) of two novel hyperchaotic systems with four-scroll attractors which have been found up to the present is investigated. Adaptive control is employed in the situation that system parameters are unknown. Based on Lyapunov stability theory, an adaptive controller and a parameter update law are designed so that the two systems can be synchronized asymptotically by FPS. Numerical simulation is provided to show the effectiveness of the proposed adaptive controller and the parameter update law.

scholarly journals Modified Function Projective Synchronization of Financial Hyperchaotic Systems via Adaptive Impulsive Controller with Unknown Parameters

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Guoliang Cai ◽  
Lingling Zhang ◽  
Lan Yao ◽  
Xiulei Fang
Keyword(s):  
Sufficient Conditions ◽  
Impulsive System ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Modified Function Projective Synchronization ◽  
The Stability ◽  
Hyperchaotic Systems

Modified function projective synchronization via adaptive impulsive controller between two different financial hyperchaotic systems is investigated, where the external uncertainties are considered. The updated laws of the unknown parameters are given and the sufficient conditions are deduced based on Lyapunov stability theorem and the stability analysis of impulsive system. Finally, the two financial hyperchaotic systems are taken for example and the numerical examples are worked through for illustrating the main results.

GENERALIZED PROJECTIVE SYNCHRONIZATION OF A CLASS OF DELAYED NEURAL NETWORKS

2008 ◽  
Vol 22 (03) ◽  
pp. 181-190 ◽  
Author(s):  
JUAN MENG ◽  
XINGYUAN WANG
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Generalized Projective Synchronization

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

scholarly journals A Novel Scheme Adaptive Hybrid Dislocated Synchronization for Two Identical and Different Memristor Chaotic Oscillator Systems with Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jie Chen ◽  
Junwei Sun ◽  
Ming Chi ◽  
Xin-Ming Cheng
Keyword(s):  
Chaos Synchronization ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Parameters Estimation ◽  
Drive System ◽  
Projective Synchronization ◽  
Chaotic Oscillator ◽  
Uncertain Parameters ◽  
State Variables ◽  
Response System

The drive system can synchronize with the response system by the scaling factor in the traditional projective synchronization. This paper proposes a novel adaptive hybrid dislocated synchronization with uncertain parameters scheme for chaos synchronization using the Lyapunov stability theory. The drive system is synchronized by the sum of hybrid dislocated state variables for the response system. By designing effective hybrid dislocated adaptive controller and hybrid dislocated adaptive law of the parameters estimation, we investigate the synchronization of two identical memristor chaotic oscillator systems and two different memristor chaotic oscillator systems with uncertain parameters. Finally, the numerical simulation examples are provided to show the effectiveness of our method.

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.

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