scholarly journals On the Impulsive Synchronization Control for a Class of Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Bo Wang ◽  
Peng Shi ◽  
Xiucheng Dong
Keyword(s):  
Numerical Simulation ◽  
Control Theory ◽  
Lyapunov Functional ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Synchronization Control ◽  
Practical Application ◽  
Impulsive Synchronization ◽  
Theoretical Results

The problem on chaos synchronization for a class of chaotic system is addressed. Based on impulsive control theory and by constructing a novel Lyapunov functional, new impulsive synchronization strategies are presented and possess more practical application value. Finally some typical numerical simulation examples are included to demonstrate the effectiveness of the theoretical results.

The Model of Liu Chaotic Synchronization with Oscillating Parameters under the Impulsive Control

2011 ◽  
Vol 480-481 ◽  
pp. 1378-1382
Author(s):  
Yan Hui Chen
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Impulsive Differential Equations ◽  
Chaotic Synchronization ◽  
Control Signal ◽  
Synchronization Control ◽  
Security Risks ◽  
Control Scheme

The control of chaotic synchronization is the kernel technology in chaos-based secure communication. Those control methods have to transmitting control signal which increase the security risks of the communication system. Attacker can reconstruct the chaotic system or estimate parameters by using the information of the chaotic system. In this paper we propose a hybrid Liu chaotic synchronization control scheme which contains both continuous chaotic system with oscillating parameters approach to 0 and discrete chaotic system. By theory of impulsive differential equations, we proved a theorem that two continuous Liu chaotic systems can get synchronized without control signal transmitting which has reduced the risk of the security.

PRACTICAL STABILITY OF IMPULSIVE SYNCHRONIZATION BETWEEN TWO NONAUTONOMOUS CHAOTIC SYSTEMS

2000 ◽  
Vol 10 (04) ◽  
pp. 859-867 ◽  
Author(s):  
TAO YANG ◽  
LEON O. CHUA
Keyword(s):  
Differential Equation ◽  
Impulsive Differential Equation ◽  
Chaotic Systems ◽  
Practical Stability ◽  
Time Interval ◽  
Theoretical Methods ◽  
Synchronization Errors ◽  
Impulsive Synchronization ◽  
Error System ◽  
Theoretical Results

The practical stability of impulsive synchronization between two nonautonomous chaotic systems is studied in this paper, and this is equivalent to that of the origin of the synchronization error system, which is modeled by an impulsive differential equation. We develop theoretical methods of choosing the time interval between two successive synchronization impulses and strengths of synchronization impulses for restricting synchronization errors within prescribed regions around the origin. Numerical experimental results are given to demonstrate theoretical results.

scholarly journals Projective Synchronization of Chaotic Systems Via Backstepping Design

2013 ◽  
Vol 18 (3) ◽  
pp. 965-973 ◽  
Author(s):  
A. Tarai ◽  
M.A. Khan
Keyword(s):  
Numerical Simulation ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Discrete Dynamical Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Backstepping Design ◽  
Simulation Results ◽  
Duffing Map

Abstract Chaos synchronization of discrete dynamical systems is investigated. An algorithm is proposed for projective synchronization of chaotic 2D Duffing map and chaotic Tinkerbell map. The control law was derived from the Lyapunov stability theory. Numerical simulation results are presented to verify the effectiveness of the proposed algorithm

SYNCHRONIZATION CONTROL FOR A CLASS OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2005 ◽  
Vol 15 (07) ◽  
pp. 2235-2246 ◽  
Author(s):  
HER-TERNG YAU ◽  
JUI-SHENG LIN ◽  
JUN-JUH YAN
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Sliding Mode ◽  
Variable Structure ◽  
Synchronization Control ◽  
Control Law ◽  
Structure Control ◽  
Synchronization Problem ◽  
Error State

This paper investigates the chaos synchronization problem for a class of uncertain master-slave chaotic systems. Based on the variable structure control theory, a strategy is proposed to guarantee the occurrence of a sliding mode motion of error states when the proposed control law is applied. As expected, the error state is able to drive to zero with match external uncertainties or into a predictable neighborhood of zero with mismatch external uncertainties. Furthermore, a modified continuous sliding mode controller is also proposed to avoid the chattering. Examples of Lorenz system and Chua's circuit are presented to demonstrate the obtained results.

scholarly journals Hybrid H-infinity synchronization for uncertain continuous chaotic systems based on digital redesign approach

2021 ◽  
pp. 002029402110211
Author(s):  
Jiunn-Shiou Fang ◽  
Jason Sheng-Hong Tsai ◽  
Jun-Juh Yan ◽  
Li-Huseh Chiang ◽  
Shu-Mei Guo
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Design Procedure ◽  
Upper Bounds ◽  
Synchronization Control ◽  
H Infinity ◽  
Saturation Function ◽  
Digital Redesign ◽  
Sliding Mode Controllers

In this paper, the design of hybrid H-infinity synchronization control for continuous chaotic systems based on sliding mode control (SMC) is considered. H-infinity discrete sliding mode controllers integrated with the digital redesign approach are newly designed to achieve robust chaos synchronization. By the proposed design procedure, an H-infinity discrete-time SMC can be easily obtained to guarantee the robustness of synchronization even if the system is disturbed with unmatched perturbations. Besides, since the saturation function is adopted to eliminate the unexpected chattering phenomenon, this paper also discusses the effect of saturation function in multi-input multi-output (MIMO) SMC and the upper bounds of sliding mode trajectories are obtained which is not indicated in the literature. Finally, we perform the simulation to verify the effectiveness of the proposed controller.

FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL

2011 ◽  
Vol 22 (11) ◽  
pp. 1281-1291 ◽  
Author(s):  
RANCHAO WU ◽  
DONGXU CAO
Keyword(s):  
Numerical Simulation ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Simulation Results ◽  
Invariant Principle

In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

IMPULSIVE SYNCHRONIZATION AND ITS IMPLEMENTATION IN CHEN–LEE SYSTEMS

2011 ◽  
Vol 25 (29) ◽  
pp. 3893-3903 ◽  
Author(s):  
LAP-MOU TAM ◽  
SENG-KIN LAO ◽  
LONG-JYE SHEU ◽  
HSIEN-KENG CHEN
Keyword(s):  
Numerical Simulation ◽  
Electronic Circuit ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Impulsive Synchronization ◽  
Lyapunov’S Direct Method ◽  
Global Exponential Synchronization ◽  
Theoretical Results

The impulsive synchronization of two chaotic Chen–Lee systems was investigated in this paper. Based on Lyapunov's direct method, sufficient conditions for the global exponential synchronization and global asymptotical synchronization were derived. Further, the theoretical results were verified by a numerical simulation. In addition, the impulsive synchronization of two chaotic Chen–Lee systems was also implemented using an electronic circuit.

scholarly journals Stabilization and Synchronization of Unified Chaotic System via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Cheng Hu ◽  
Haijun Jiang
Keyword(s):  
Control Theory ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Impulsive Control ◽  
Auxiliary Function ◽  
Unified Chaotic System ◽  
Piecewise Continuous ◽  
Control And Synchronization ◽  
Theoretical Results

The impulsive control and synchronization of unified chaotic system are proposed. By applying impulsive control theory and introducing a piecewise continuous auxiliary function, some novel and useful conditions are provided to guarantee the globally asymptotical stabilization and synchronization of unified chaotic system under impulsive control. Compared with some previous results, our criteria are superior and less conservative. Finally, the effectiveness of theoretical results is shown through numerical simulations.

scholarly journals Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Limin Zou ◽  
Yang Peng ◽  
Yuming Feng ◽  
Zhengwen Tu
Keyword(s):  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Condition ◽  
Numerical Examples ◽  
Impulsive Synchronization ◽  
Chaotic Circuits ◽  
The Stability ◽  
Control And Synchronization

The purpose of this note is to study impulsive control and synchronization of memristor based chaotic circuits shown by Muthuswamy. We first establish a less conservative sufficient condition for the stability of memristor based chaotic circuits. After that, we discuss the effect of errors on stability. Meanwhile, we also discuss impulsive synchronization of two memristor based chaotic systems. Our results are more general and more applicable than the ones shown by Yang, Li, and Huang. Finally, several numerical examples are given to show the effectiveness of our methods.

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