scholarly journals A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm

2015 ◽  
Vol 5 (1) ◽  
pp. 739-747 ◽  
Author(s):  
I. Ahmad ◽  
A. Saaban ◽  
A. Ibrahin ◽  
M. Shahzad
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Closed Loop System ◽  
Feedback Controllers ◽  
Control Techniques ◽  
Synchronization Problem ◽  
Response Systems ◽  
Globally Stable ◽  
Time Evaluation

The problem of chaos synchronization is to design a coupling between two chaotic systems (master-slave/drive-response systems configuration) such that the chaotic time evaluation becomes ideal and the output of the slave (response) system asymptotically follows the output of the master (drive) system. This paper has addressed the chaos synchronization problem of two chaotic systems using the Nonlinear Control Techniques, based on Lyapunov stability theory. It has been shown that the proposed schemes have outstanding transient performances and that analytically as well as graphically, synchronization is asymptotically globally stable. Suitable feedback controllers are designed to stabilize the closed-loop system at the origin. All simulation results are carried out to corroborate the effectiveness of the proposed methodologies by using Mathematica 9.

CHAOS SYNCHRONIZATION OF TWO COUPLED DYNAMOS SYSTEMS WITH UNKNOWN SYSTEM PARAMETERS

2004 ◽  
Vol 15 (06) ◽  
pp. 873-883 ◽  
Author(s):  
H. N. AGIZA
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Error Feedback ◽  
Simple Criterion ◽  
Global Synchronization ◽  
System Parameters ◽  
Synchronization Problem ◽  
Unknown System

This paper addresses the synchronization problem of two coupled dynamos systems in the presence of unknown system parameters. Based on Lyapunov stability theory, an active control law is derived and activated to achieve the state synchronization of two identical coupled dynamos systems. By using Gerschgorin theorem, a simple generic criterion is derived for global synchronization of two coupled dynamos systems with a unidirectional linear error feedback coupling. This simple criterion is applicable to a large class of chaotic systems, where only a few algebraic inequalities are involved. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

ADAPTIVE OBSERVER BASED SYNCHRONIZATION OF A CLASS OF UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 18 (08) ◽  
pp. 2425-2435 ◽  
Author(s):  
SAMUEL BOWONG ◽  
RENÉ YAMAPI
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Observer ◽  
Adaptive Synchronization ◽  
External Disturbances ◽  
Parameter Mismatch ◽  
Lipschitz Constants ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Robust Adaptive

This study addresses the adaptive synchronization of a class of uncertain chaotic systems in the drive-response framework. For a class of uncertain chaotic systems with parameter mismatch and external disturbances, a robust adaptive observer based on the response system is constructed to practically synchronize the uncertain drive chaotic system. Lyapunov stability theory ensures the practical synchronization between the drive and response systems even if Lipschitz constants on function matrices and bounds on uncertainties are unknown. Numerical simulation of two illustrative examples are given to verify the effectiveness of the proposed method.

scholarly journals Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Lin Wang ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Closed Loop ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Closed Loop System ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Lyapunov Stability Criterion ◽  
Theoretical Results

Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results.

scholarly journals Locally and Globally Exponential Synchronization of Moving Agent Networks by Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Lifu Wang ◽  
Peng Xue ◽  
Zhi Kong ◽  
Xingang Wang
Keyword(s):  
Dimensional Space ◽  
Lyapunov Stability Theory ◽  
Exponential Synchronization ◽  
Time Varying ◽  
Feedback Controllers ◽  
Adaptive Feedback ◽  
Fast Switching ◽  
Synchronization Problem ◽  
Agent Networks ◽  
New Criteria

The exponential synchronization problem is investigated for a class of moving agent networks in a two-dimensional space and exhibits time-varying topology structure. Based on the Lyapunov stability theory, adaptive feedback controllers are developed to guarantee the exponential synchronization between each agent node. New criteria are proposed for verifying the locally and globally exponential synchronization of moving agent networks under the constraint of fast switching. In addition, a numerical example, including typical moving agent network with the Rössler system at each agent node, is provided to demonstrate the effectiveness and applicability of the proposed design approach.

scholarly journals Pinning Two Nonlinearly Coupled Complex Networks with an Asymmetrical Coupling Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwen Feng ◽  
Ze Tang ◽  
Jingyi Wang ◽  
Yi Zhao
Keyword(s):  
Complex Networks ◽  
Lyapunov Stability Theory ◽  
Pinning Control ◽  
Feedback Controllers ◽  
Dynamical Networks ◽  
Synchronization Problem ◽  
Response Network ◽  
Control Schemes ◽  
Hybrid Synchronization ◽  
Theoretical Results

This paper addresses the hybrid synchronization problem in two nonlinearly coupled complex networks with asymmetrical coupling matrices under pinning control schemes. The hybrid synchronization of two complex networks is the outer antisynchronization between the driving network and the response network while the inner complete synchronization in the driving network and the response network. We will show that only a small number of pinning feedback controllers acting on some nodes are effective for synchronization control of the mentioned dynamical networks. Based on Lyapunov Stability Theory, some simple criteria for hybrid synchronization are derived for such dynamical networks by pinning control strategy. Numerical examples are provided to illustrate the effectiveness of our theoretical results.

Synchronization Controlling for a Permanent Magnet Synchronous Motor via Linear Feedback with Single State

2012 ◽  
Vol 442 ◽  
pp. 472-476 ◽  
Author(s):  
Ji Gui Jian ◽  
Zhi Hua Zhao ◽  
Wei Wei Wang
Keyword(s):  
Permanent Magnet ◽  
Chaotic Systems ◽  
Permanent Magnet Synchronous Motor ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Synchronous Motor ◽  
Exponential Synchronization ◽  
Linear Feedback ◽  
Control Approach ◽  
Synchronization Problem

This paper treats the globally exponential synchronization problem of the permanent magnet synchronous motor chaotic system. Based on Lyapunov stability theory and some inequalities techniques, one novel control approach, namely linear feedback control with one state is proposed to realize the globally exponential synchronization of two permanent magnet synchronous motor chaotic systems. In this case, some sufficient conditions for the globally exponential synchronization of two chaotic systems are obtained analytically. The controllers here designed have simple structure and less conservation. The numerical simulation results show the effectiveness of the method.

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 BETWEEN TWO DIFFERENT HYPERCHAOTIC SYSTEMS WITH UNCERTAIN PARAMETERS

2013 ◽  
Vol 27 (13) ◽  
pp. 1350044
Author(s):  
XING-YUAN WANG ◽  
YU-HONG YANG ◽  
MING-KU FENG
Keyword(s):  
Lyapunov Stability ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Sufficient Condition ◽  
Uncertain Parameters ◽  
Hyperchaotic Lorenz System ◽  
Hyperchaotic Systems

This paper studies the problem of chaos synchronization between two different hyperchaotic systems with uncertain parameters. Based on the Lyapunov stability theory, we obtain the sufficient condition of synchronization between two different hyperchaotic systems with uncertain parameters. A new adaptive controller with parameter update laws is designed to synchronize these chaotic systems. We proved it in theory with an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Rössler system. Numerical results verified the validation of the proposed scheme.

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.

ADAPTIVE ROBUST SYNCHRONIZATION FOR A CLASS OF DIFFERENT UNCERTAIN CHAOTIC SYSTEMS

2008 ◽  
Vol 22 (23) ◽  
pp. 4069-4082 ◽  
Author(s):  
XINGYUAN WANG ◽  
MINGJUN WANG
Keyword(s):  
Chaotic Systems ◽  
Adaptive Controller ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Robust Controller ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Response Systems ◽  
Uncertain Chaotic Systems ◽  
Predicted Values

This paper addresses the adaptive synchronization problem of a class of different uncertain chaotic systems. A general adaptive robust controller and parameters update rule are designed. It is proved theoretically that the controller and update rule can make the drive-response systems with different structures asymptotically synchronized, and change the unknown parameters to constants when noise exists. When the drive system is certain, the unknown parameters of the response system can be updated to the predicted values. The results of numerical simulations show the effectiveness of the adaptive controller.

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