H_Infinity Anti-Synchronization of Chaotic Systems with Unknown Parameters

2013 ◽  
Vol 336-338 ◽  
pp. 528-531 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Hui Zhang
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Chaotic Systems ◽  
External Disturbance ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Lyapunov Control ◽  
Norm Constraint ◽  
General Method

In this paper, a general method is proposed for the anti-synchronization of chaotic systems with unknown parameters. This approach is based on the Lyapunov control theory, and employs a combination of feedback control and adaptive control. With this method, the unknown parameters is estimated and the adaptive feedback controller is designed to not only guarantee stable anti-synchronization but also reduce the effect of external disturbance to an norm constraint. Numerical simulations results are presented to demonstrate the effectiveness of the method.

An H_Infinity Approach to Synchronization of Chaotic Systems

2013 ◽  
Vol 756-759 ◽  
pp. 3874-3878
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Chang Chun Sun ◽  
Zheng Yu Li
Keyword(s):  
Adaptive Control ◽  
Lyapunov Function ◽  
Control Theory ◽  
General Class ◽  
Function Method ◽  
Chaotic Systems ◽  
External Disturbance ◽  
Adaptive Controller ◽  
Lyapunov Function Method ◽  
Norm Constraint

In this paper, a new adaptive approach for H_infinity synchronization of a general class of chaotic systems. Based on adaptive control theory and Lyapunov function method, An adaptive controller is constructed, the H_infinity synchronization controller is presented to not only guarantee stable synchronization but also reduce the effect of external disturbance to an H_infinity norm constraint. The results of simulation are given to show effectiveness of the proposed method.

scholarly journals Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. M. El-Dessoky ◽  
M. T. Yassen
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Feedback Control ◽  
Chaos Control ◽  
Control Technique ◽  
Unknown Parameters ◽  
Chaotic Dynamical System ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control And Synchronization

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.

scholarly journals Anti-Synchronization of Tigan and Li Systems with Unknown Parameters via Adaptive Control

2011 ◽  
Vol 2 (1) ◽  
pp. 17-28
Author(s):  
Vaidyanathan SUNDARAPANDIAN ◽  
Karthikeyan RAJAGOPAL
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Adaptive Synchronization ◽  
Control Law ◽  
Slave System ◽  
Unknown Parameters ◽  
Master System ◽  
Uncertain Chaotic Systems

In this paper, we apply adaptive control method toderive new results for the anti-synchronization of identical Tigansystems (2008), identical Li systems (2009) and non-identical Tiganand Li systems. In adaptive anti-synchronization of identical chaoticsystems, the parameters of the master and slave systems are unknownand we devise feedback control law using the estimates of the systemparameters. In adaptive anti-synchronization of non-identical chaoticsystems, the parameters of the master system are known, but theparameters of the slave system are unknown and we devise feedbackcontrol law using the estimates of the parameters of the slave system.Our adaptive synchronization results derived in this paper for theuncertain Tigan and Li systems are established using Lyapunovstability theory. Since the Lyapunov exponents are not required forthese calculations, the adaptive control method is very effective andconvenient to achieve anti-synchronization of identical and nonidenticalTigan and Li systems. Numerical simulations are shown todemonstrate the effectiveness of the adaptive anti-synchronizationschemes for the uncertain chaotic systems addressed in this paper.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

2008 ◽  
Vol 22 (24) ◽  
pp. 4175-4188 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
LIANG CHEN
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Chaotic Systems ◽  
Stochastic Perturbation ◽  
Projective Synchronization ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Communication Scheme ◽  
Simulation Results ◽  
Feedback Method

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

Stabilization of a Class of Chaotic Systems via Single-State Adaptive Feedback Controller

2014 ◽  
Vol 571-572 ◽  
pp. 965-968
Author(s):  
De Gang Yang ◽  
Guo Ying Qiu
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Feedback Controller ◽  
Control Analysis ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Feedback Control Method ◽  
Single State ◽  
System States

This paper investigates the application of the adaptive feedback control method in the chaotic system and Single-state Adaptive Feedback Controller. We divide the adaptive feedback controller into several items, each of which has only one component of the system states as feedback input into each dimension of the system. With the introduction of single-state controller, the scale of control inputs can be flexibly adjusted, the additional loading reduced, better convergence effect obtained and the application field of adaptive feedback control methods further extended in stable control analysis of chaotic systems. An example is also given to illustrate the validity of our result.

scholarly journals Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system

2015 ◽  
Vol 25 (3) ◽  
pp. 333-353 ◽  
Author(s):  
Sundarapandian Vaidyanathan ◽  
Christos Volos
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Phase Portraits ◽  
The Novel ◽  
Unknown Parameters ◽  
Mathematical Properties ◽  
Quadratic Nonlinearities

AbstractFirst, this paper announces a seven-term novel 3-D conservative chaotic system with four quadratic nonlinearities. The conservative chaotic systems are characterized by the important property that they are volume conserving. The phase portraits of the novel conservative chaotic system are displayed and the mathematical properties are discussed. An important property of the proposed novel chaotic system is that it has no equilibrium point. Hence, it displays hidden chaotic attractors. The Lyapunov exponents of the novel conservative chaotic system are obtained as L1= 0.0395,L2= 0 and L3= −0.0395. The Kaplan-Yorke dimension of the novel conservative chaotic system is DKY=3. Next, an adaptive controller is designed to globally stabilize the novel conservative chaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical conservative chaotic systems with unknown parameters. MATLAB simulations have been depicted to illustrate the phase portraits of the novel conservative chaotic system and also the adaptive control results.

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