ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE UNIFIED CHAOTIC SYSTEM

2009 ◽  
Vol 23 (15) ◽  
pp. 1913-1921 ◽  
Author(s):  
XINGYUAN WANG ◽  
JUNMEI SONG
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Response System ◽  
Unified Chaotic System ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper studies the adaptive full state hybrid projective synchronization method. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with known or unknown parameters asymptotically full state hybrid projective synchronized. A unified chaotic system is used as an example and numerical simulations show the effectiveness of the scheme.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION OF UNIFIED CHAOTIC SYSTEM WITH UNKNOWN PARAMETERS

2011 ◽  
Vol 25 (32) ◽  
pp. 4661-4666 ◽  
Author(s):  
XING-YUAN WANG ◽  
LE-BIAO ZHU
Keyword(s):  
Dynamical System ◽  
Chaotic System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Response System ◽  
Unified Chaotic System ◽  
Full State ◽  
Hybrid Projective Synchronization

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme.

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.

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.

scholarly journals Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Tao Wang ◽  
Kejun Wang ◽  
Nuo Jia
Keyword(s):  
Chaotic System ◽  
Chaos Control ◽  
Control Strategies ◽  
Direct Method ◽  
Projective Synchronization ◽  
Complete Synchronization ◽  
Unknown Parameters ◽  
Feedback Controllers ◽  
Adaptive Parameter ◽  
Hybrid Projective Synchronization

Adaptive feedback controllers based on Lyapunov's direct method for chaos control and hybrid projective synchronization (HPS) of a novel 3D chaotic system are proposed. Especially, the controller can be simplified ulteriorly into a single scalar one to achieve complete synchronization. The HPS between two nearly identical chaotic systems with unknown parameters is also studied, and adaptive parameter update laws are developed. Numerical simulations are demonstrated to verify the effectiveness of the control strategies.

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.

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.

Modified Projective Synchronization of Chaotic Systems with Unknown Parameters

2011 ◽  
Vol 128-129 ◽  
pp. 1182-1185
Author(s):  
Min Xiu Yan ◽  
Li Ping Fan
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Adaptive Sliding Mode Control ◽  
Unknown Parameters ◽  
Response System ◽  
Uncertain Chaotic Systems ◽  
Modified Projective Synchronization

This paper proposes the modified projective synchronization of uncertain chaotic systems with unknown parameters via active adaptive sliding mode control (AASMC). The disturbances are considered both in the drive and the response system. The bounds of the disturbances are unknown. The adaptive updating laws are designed to tackle the unknown parameters. Moreover, the robustness and stability of the proposed AASMC is proved by the Lyapunov stability theory. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed scheme.

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