SYNCHRONIZATION OF MODIFIED CHEN SYSTEM

2004 ◽  
Vol 14 (11) ◽  
pp. 3969-3979 ◽  
Author(s):  
E. M. ELABBASY ◽  
H. N. AGIZA ◽  
M. M. EL-DESSOKY
Keyword(s):  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
Chen System ◽  
Control Laws ◽  
System Parameters ◽  
Synchronization Problem ◽  
Unknown System

This paper addresses the synchronization problem of two modified Chen systems in the presence of unknown system parameters. One-way coupling and active control laws are applied to achieve the state synchronization of two identical modified Chen systems. Based on Lyapunov stability theory, active control laws are derived such that the two modified Chen systems are to be synchronized. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

ANTI-SYNCHRONIZATION OF UNIFIED HYPERCHAOTIC SYSTEMS

2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG
Keyword(s):  
Adaptive Control ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Lyapunov Stability Theory ◽  
Control Methods ◽  
System Parameters ◽  
Hyperchaotic Systems ◽  
Active Control Method

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.

scholarly journals Euler’s Equations of Rigid Body: Its Control and Synchronization using Active Control and Recursive Backstepping methods.

2018 ◽  
Vol 5 (1) ◽  
Author(s):  
Cornelius Ogab ◽  
Babatunde Idowu ◽  
Abiola Ogungbe ◽  
Eugene Onori ◽  
Olufunmilayo Ometan ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Steady State ◽  
Rigid Body ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Control Laws ◽  
Control And Synchronization ◽  
Methods Numerical

We present Euler’s Equation of Rigid Body, its control and synchronization using active control and recursive backstepping methods. Based on Lyapunov stability theory, control laws are derived to synchronize the chaotic system and also to control to a steady state as well as track to a desired function via recursive backstepping methods. Numerical simulation are shown to verify the results.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM

2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU
Keyword(s):  
Adaptive Control ◽  
Parameter Identification ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Uncertain Parameters ◽  
Chen System ◽  
Adaptive Control Law

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

Active Anti-Synchronization Between Identical and Distinctive Hyperchaotic Systems

2008 ◽  
Vol 15 (04) ◽  
pp. 371-382 ◽  
Author(s):  
M. M. Al-sawalha ◽  
M. S. M. Noorani
Keyword(s):  
Theoretical Analysis ◽  
Active Control ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
High Dimensional ◽  
Analysis Strategy ◽  
Relevant Variables ◽  
Hyperchaotic Systems

This paper brings attention to hyperchaos anti-synchronization between two identical and distinctive hyperchaotic systems using active control theory. The sufficient conditions for achieving anti-synchronization of two high dimensional hyperchaotic systems is derived based on Lyapunov stability theory, where the controllers are designed by using the sum of relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis strategy.

scholarly journals Adaptive Synchronization of Chaotic SC-CNN with Uncertain State Template

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Phuong Dam Thanh ◽  
Cat Pham Thuong
Keyword(s):  
Neural Network ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Cellular Neural Network ◽  
Uncertain Parameter ◽  
Adaptive Synchronization ◽  
Chaotic State ◽  
Control Laws

The problem of synchronization of chaotic State Controlled Cellular Neural Network (SC-CNN) with uncertain state template is investigated. In detail, the following three cases are solved: firstly, synchronization of two identical chaotic SC-CNNs with uncertain state template, secondly, synchronization of two nonidentical chaotic SC-CNNs with all uncertain state templates, and, thirdly, synchronization between chaotic SC-CNN with uncertain state template and different uncertain parameter chaotic systems. The controllers and update laws proposed in each case are proved closely based on Lyapunov stability theory. In addition, some illustrative corresponding examples are presented to demonstrate the effectiveness and usefulness of the proposed control laws.

scholarly journals Hybrid synchronisation of vallis chaotic systems using nonlinear active control

2018 ◽  
Vol 7 (2.21) ◽  
pp. 50 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Vikash Kumar ◽  
Eshan Tiwari ◽  
Vinay K. Chauhan
Keyword(s):  
Numerical Simulation ◽  
Active Control ◽  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Southern Oscillation ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
Control Laws ◽  
Relevant Variables ◽  
Simulation Results

In this paper, hybrid synchronisation of Vallis chaotic systems using a nonlinear control technique is proposed. Vallis system represents the principal quantitative features of the El-Nino Southern Oscillation (ENSO) phenomenon. A nonlinear active control technique is used for hybrid synchronisation. Control laws are designed by using the sum of the relevant variables of the both mater and slave systems. Required Lyapunov stability condition is devised using Lyapunov stability theory. Numerical simulation results reflect the successful achievement of the proposed objectives. MATLAB is used for simulation.  

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.

PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION CONTROL OF A LORENZ-LIKE SYSTEM

2008 ◽  
Vol 22 (15) ◽  
pp. 2453-2461 ◽  
Author(s):  
XINGYUAN WANG ◽  
YONG WANG
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Uncertain System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Synchronization Control ◽  
System Parameters

This paper analyzes the synchronization control of new chaotic systems called Lorenz-like systems. Based on the Lyapunov stability theory, an adaptive controller and a parameter update rule are designed. It is proved that the controller and update rule not only achieve self-synchronization of Lorenz-like systems but can also make the Lorenz-like system asymptotically synchronized with the Rössler system, and further identify the uncertain system parameters. Numerical simulations have shown the effectiveness of the adaptive controller.

Outer synchronization of general colored networks with different-dimensional node via sliding mode control

2018 ◽  
Vol 32 (31) ◽  
pp. 1850342 ◽  
Author(s):  
Shuang Liu ◽  
Qingyun Wang
Keyword(s):  
Lyapunov Stability ◽  
Stability Theory ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Sliding Mode Controller ◽  
Network Systems ◽  
Colored Complex ◽  
System Parameters ◽  
Linear Subsystem

In this paper, a separated sliding mode strategy is proposed for the synchronization of network systems. To break the predicament caused by the inhomogeneity of nodes coupling in complex network, a colored network with different node systems and edges is given. According to the nonlinear subsystem of the colored complex networks, a separated sliding mode controller is designed, while for the linear subsystem, some appropriate system parameters are established to implement synchronization. Then, based on the Lyapunov stability theory, the performance of the sliding mode controller is appraised through the synchronization for the colored networks consisting of different-dimensional systems and nonidentical interactions. In the end, two simulation illustrations are employed to demonstrate the presented control method.

Sign in / Sign up

Export Citation Format

Share Document