scholarly journals Projection Synchronization of a Class of Complex Chaotic Systems with Both Uncertainty and Disturbance

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hongsheng Sha ◽  
Guijuan Wang ◽  
Tao Hao ◽  
Zuoxun Wang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Control Method ◽  
Linear Feedback ◽  
Second Step ◽  
Disturbance Estimation ◽  
Linear Feedback Controller ◽  
Feedback Method ◽  
Complex Chaotic Systems ◽  
Uncertainty And Disturbance Estimation

This paper mainly investigates the projection synchronization of complex chaotic systems with both uncertainty and disturbance. Using the linear feedback method and the uncertainty and disturbance estimation- (UDE-) based control method, the projection synchronization of such systems is realized by two steps. In the first step, a linear feedback controller is designed to control the nominal complex chaotic systems to achieve projection synchronization. An UDE-based controller is proposed to estimate the whole of uncertainty and disturbance in the second step. Finally, numerical simulations verify the feasibility and effectiveness of the control method.

scholarly journals Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

2014 ◽  
Vol 65 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Rajagopal Karthikeyan ◽  
Vaidyanathan Sundarapandian
Keyword(s):  
Numerical Simulations ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Hybrid Synchronization ◽  
Active Control Method

Abstract This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

scholarly journals Enhanced Symplectic Synchronization between Two Different Complex Chaotic Systems with Uncertain Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng-Hsiung Yang
Keyword(s):  
Numerical Simulations ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Asymptotical Stability ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Null Solution ◽  
Special Cases ◽  
Error Dynamics ◽  
Complex Chaotic Systems

An enhanced symplectic synchronization of complex chaotic systems with uncertain parameters is studied. The traditional chaos synchronizations are special cases of the enhanced symplectic synchronization. A sufficient condition is given for the asymptotical stability of the null solution of error dynamics. The enhanced symplectic synchronization may be applied to the design of secure communication. Finally, numerical simulations results are performed to verify and illustrate the analytical results.

Linear feedback controller design method for time-delay chaotic systems

2012 ◽  
Vol 70 (1) ◽  
pp. 355-362 ◽  
Author(s):  
Hua Wang ◽  
Xin Wang ◽  
Xiao-Jin Zhu ◽  
Xiao-Hua Wang
Keyword(s):  
Time Delay ◽  
Chaotic Systems ◽  
Controller Design ◽  
Design Method ◽  
Feedback Controller ◽  
Linear Feedback ◽  
Linear Feedback Controller

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

scholarly journals Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhi Liu ◽  
Rongwei Guo
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Linear Feedback ◽  
Dynamic Feedback ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Complex Chaotic Systems ◽  
Complex Chaotic System ◽  
Theoretical Results

The stabilization problem of the complex chaotic system is investigated in this paper. First, a systematic method is proposed, by which a given complex chaotic system can be transformed into its equivalent real chaotic system. Then, both simple and physical controller is designed for the corresponding real chaotic system by the dynamic feedback control method, thereby the controller for the original complex chaotic system is obtained. Especially, for some complex system, the controller is obtained by the linear feedback control method. Finally, two illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

scholarly journals Antisynchronization of the Hyperchaotic Systems with Uncertainty and Disturbance Using the UDE-Based Control Method

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Zuoxun Wang ◽  
Xiaotong Yu ◽  
Guijuan Wang
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
External Disturbance ◽  
Hyperchaotic System ◽  
Dynamic Feedback ◽  
Disturbance Estimation ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Hyperchaotic Systems ◽  
Uncertainty And Disturbance Estimation

In this paper, we investigate the antisynchronization problem of a class of hyperchaotic systems with both model uncertainty and external disturbance. Firstly, combining the dynamic feedback control method and the uncertainty and disturbance estimation (UDE)-based control method, we propose a new UDE-based dynamic feedback control method. Secondly, we take the 4D hyperchaotic system as an example and realize the antisynchronization problem of such system. Finally, the effectiveness and correctness of the proposed method is verified by numerical simulation.

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.

Modified Projective Synchronization of Uncertain Unified Chaotic Systems via Backstepping Approach

2011 ◽  
Vol 66-68 ◽  
pp. 1136-1141
Author(s):  
R. Z. Luo ◽  
Y. L. Wang ◽  
S. C. Deng
Keyword(s):  
Numerical Simulations ◽  
Unknown Parameter ◽  
Chaotic Systems ◽  
Control Method ◽  
Backstepping Control ◽  
Projective Synchronization ◽  
Control Technique ◽  
Unified Chaotic Systems ◽  
Backstepping Approach ◽  
Modified Projective Synchronization

This paper focuses on modified projective synchronization of uncertain unified chaotic systems via backstepping approach. A parameter observer is designed to identify the unknown parameter of unified chaotic systems and a novel backstepping control method is presented for synchronizing two identical unified chaotic systems with each other. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control technique.

scholarly journals Targeting engineering synchronization in chaotic systems

2016 ◽  
Vol 27 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Sourav K. Bhowmick ◽  
Dibakar Ghosh
Keyword(s):  
Fixed Point ◽  
Lyapunov Function ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Scaling Factor ◽  
Linear Feedback ◽  
Generalized Synchronization ◽  
Smooth Control ◽  
Linear Feedback Controller ◽  
Linear And Nonlinear

A method of targeting engineering synchronization states in two identical and mismatch chaotic systems is explained in detail. The method is proposed using linear feedback controller coupling for engineering synchronization such as mixed synchronization, linear and nonlinear generalized synchronization and targeting fixed point. The general form of coupling design to target any desire synchronization state under unidirectional coupling with the help of Lyapunov function stability theory is derived analytically. A scaling factor is introduced in the coupling definition to smooth control without any loss of synchrony. Numerical results are done on two mismatch Lorenz systems and two identical Sprott oscillators.

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