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 Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

2020 ◽  
Vol 9 (3) ◽  
pp. 597-611
Author(s):  
Ayub Khan ◽  
Harindri Chaudhary
Keyword(s):  
Adaptive Control ◽  
Secure Communication ◽  
Chaos Control ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

Abstract In this paper, we investigate a hybrid projective combination–combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination–combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB.

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 (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.

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.

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.

FUNCTION PROJECTIVE SYNCHRONIZATION BETWEEN TWO IDENTICAL CHAOTIC SYSTEMS

2007 ◽  
Vol 18 (05) ◽  
pp. 883-888 ◽  
Author(s):  
YONG CHEN ◽  
XIN LI
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Symbolic Computation ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Active Control Method ◽  
Function Matrix

First, a function projective synchronization of two identical systems is defined. Second, based on the active control method and symbolic computation Maple, the scheme of function projective synchronization is developed to synchronize two identical chaotic systems (two identical classic Lorenz systems) up to a scaling function matrix with different initial values. Numerical simulations are used to verify the effectiveness of the scheme.

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.

scholarly journals On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Adel Ouannas
Keyword(s):  
Lyapunov Stability ◽  
Discrete Time ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Full State ◽  
Hybrid Projective Synchronization ◽  
Nonlinear Control Method

The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper.

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