Adaptive Hybrid Chaos Synchronization of Lorenz-Stenflo and 4-D Chaotic Systems with Unknown Parameters

2015 ◽  
Vol 9 (2) ◽  
Keyword(s):  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Unknown Parameters

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.

Adaptive Synchronization of Fractional Hyper-Chaotic System with Unknown Parameters

2013 ◽  
Vol 850-851 ◽  
pp. 868-871 ◽  
Author(s):  
Li Xin Yang ◽  
Wan Sheng He ◽  
Jin Ping Jia ◽  
Fan Di Zhang
Keyword(s):  
Fractional Order ◽  
Tracking Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Synchronization ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Fractional Systems ◽  
Control Approach ◽  
The Stability

In this paper, chaos synchronization of the modified Sprott E system is investigated. Based on the stability theorem for fractional systems, tracking control approach is used for the fractional-order systems with uncertain parameters. Meanwhile, suitable adaptive synchronization controller and recognizing rules of the uncertain parameters are designed. Numerical simulation results show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order hyper-chaotic systems.

ANTICIPATED FUNCTION SYNCHRONIZATION WITH UNKNOWN PARAMETERS OF DISCRETE-TIME CHAOTIC SYSTEMS

2009 ◽  
Vol 20 (04) ◽  
pp. 597-608 ◽  
Author(s):  
YIN LI ◽  
BIAO LI ◽  
YONG CHEN
Keyword(s):  
Chaotic System ◽  
Discrete Time ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Law ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems ◽  
Function Synchronization

In this paper, firstly, the control problem for the chaos synchronization of discrete-time chaotic (hyperchaotic) systems with unknown parameters are considered. Next, backstepping control law is derived to make the error signals between drive 2D discrete-time chaotic system and response 2D discrete-time chaotic system with two uncertain parameters asymptotically synchronized. Finally, the approach is extended to the synchronization problem for 3D discrete-time chaotic system with two unknown parameters. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

Adaptive Synchronization of Chaotic Genesio–Tesi Systems Via A Nonlinear Control

2018 ◽  
Vol 7 (3.19) ◽  
pp. 136
Author(s):  
Esmat Sadat Alaviyan Shahri
Keyword(s):  
Nonlinear Control ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Adaptive Synchronization ◽  
Unknown Parameters ◽  
Control Effort ◽  
Analysis And Design ◽  
Synchronization Problem ◽  
Synchronization Scheme

The paper presents the stabilization and adaptive synchronization problem of a class of chaotic systems (Genesio–Tesi system) with three unknown parameters. A novel nonlinear control effort is proposed and an adaptive strategy is presented in order to the states of two Genesio–Tesi systems were asymptotically synchronized. The known Lyapunov method guarantees the presented stability analysis and design. An illustrative simulation result is given to demonstrate the effectiveness of the proposed chaos synchronization scheme.

scholarly journals Synchronization of an Uncertain Duffing Oscillator with Higher Order Chaotic Systems

2018 ◽  
Vol 28 (4) ◽  
pp. 625-634 ◽  
Author(s):  
Jacek Kabziński
Keyword(s):  
Adaptive Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Duffing Oscillator ◽  
Higher Order ◽  
Unknown Parameters ◽  
External Disturbances ◽  
Control Techniques ◽  
Synchronization Problems

Abstract The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing-Arneodo and Duffing-Chua synchronization problems.

scholarly journals Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiuchun Li ◽  
Jianhua Gu ◽  
Wei Xu
Keyword(s):  
Neural Network ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Original System ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
External Perturbations ◽  
Response Systems ◽  
Barbalat Lemma

Considering the effects of external perturbations on the state vector and the output of the original system, this paper proposes a new adaptive integral observer method to deal with chaos synchronization between the drive and response systems with unknown parameters. The analysis and proof are given by means of the Lyapunov stability theorem and Barbalat lemma. This approach has fewer constraints because many parameters related to chaotic system can be unknown, as shown in the paper. Numerical simulations are performed in the end and the results show that the proposed method is not only suitable to the representative chaotic systems but also applied to some neural network chaotic systems.

scholarly journals Synchronization for a Class of Uncertain Fractional Order Chaotic Systems with Unknown Parameters Using a Robust Adaptive Sliding Mode Controller

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yan Yan
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Mode Synchronization ◽  
Robust Adaptive

This paper deals with the synchronization of a class of fractional order chaotic systems with unknown parameters and external disturbance. Based on the Lyapunov stability theory, a fractional order sliding mode is constructed and a controller is proposed to realize chaos synchronization. The presented method not only realizes the synchronization of the considered chaotic systems but also enhances the robustness of sliding mode synchronization. Finally, some simulation results demonstrate the effectiveness and robustness of the proposed method.

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