Anti-Synchronization for a Modified Chen-Qi-Like Chaotic System

2012 ◽  
Vol 220-223 ◽  
pp. 2113-2116
Author(s):  
Su Hai Huang
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Stability Theorem ◽  
Control Law ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamical Characteristics ◽  
Control Scheme ◽  
Adaptive Control Scheme

A modified Chen-Qi-like chaotic system is presented. Some basic dynamical characteristics of this system are studied by calculating the Lyapunov exponent and phase figure. Based on the Lyapunov stability theorem, adaptive control scheme and parameters update law are presented for the anti-synchronization of new chaotic systems with fully unknown parameters. Finally, the numerical simulation verify that the control law and parameter changing are correct.

ADAPTIVE SWITCHING CONTROL AND SYNCHRONIZATION OF CHAOTIC SYSTEMS WITH UNCERTAINTIES

2005 ◽  
Vol 15 (10) ◽  
pp. 3381-3390 ◽  
Author(s):  
JING YAO ◽  
ZHI-HONG GUAN ◽  
DAVID J. HILL
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Switching Control ◽  
Control Law ◽  
Unknown Parameters ◽  
Control Scheme ◽  
Control And Synchronization ◽  
Adaptive Switching Control ◽  
Adaptive Control Law ◽  
Synchronization Problems

In this paper, a new adaptive switching control scheme is presented to solve control and synchronization problems. Based on Lyapunov stability theory, an adaptive control law is applied to globally stabilize chaotic systems and achieve states synchronization of two chaotic systems whose dynamics are subjected to the system disturbances and/or some unknown parameters. Simulation examples, the chaotic Chen's system and Chua's circuit, are given to show the feasibility and effectiveness of the proposed theory and method.

scholarly journals Anti-Synchronization of a Class of Chaotic Systems with Application to Lorenz System: A Unified Analysis of the Integer Order and Fractional Order

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 559 ◽  
Author(s):  
Liang Chen ◽  
Chengdai Huang ◽  
Haidong Liu ◽  
Yonghui Xia
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Finite Time ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Unknown Parameters ◽  
Integer Order ◽  
System A ◽  
Control Scheme ◽  
Lorenz Chaotic System

The paper proves a unified analysis for finite-time anti-synchronization of a class of integer-order and fractional-order chaotic systems. We establish an effective controller to ensure that the chaotic system with unknown parameters achieves anti-synchronization in finite time under our controller. Then, we apply our results to the integer-order and fractional-order Lorenz system, respectively. Finally, numerical simulations are presented to show the feasibility of the proposed control scheme. At the same time, through the numerical simulation results, it is show that for the Lorenz chaotic system, when the order is greater, the more quickly is anti-synchronization achieved.

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.

Synchronization and Parameter Identification of General Uncertain Complex Networks via Discrete Control

2014 ◽  
Vol 598 ◽  
pp. 714-717
Author(s):  
Sheng Qin Jiang ◽  
Guo Liang Cai ◽  
Shui Ming Cai
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Complex Networks ◽  
Stability Theorem ◽  
Discrete Control ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Impulse System ◽  
The Stability ◽  
Theoretical Results

This paper studies synchronization of complex networks with multi-unknown parameters and disturbances via discrete control. Based on Lyapunov stability theorem and the stability analysis of impulse system, adaptive-impulse synchronization criteria for general multi-uncertain complex networks have been established. Finally, a numerical simulation is provided to support the theoretical results.

Stabilization of Chaotic System with Uncertain Parameters

2011 ◽  
Vol 66-68 ◽  
pp. 217-219
Author(s):  
Wei Ming Sun ◽  
Xin Yu Wang ◽  
Jun Wei Lei
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Adaptive Strategy ◽  
Stability Theorem ◽  
Convergence Time ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Unknown Parameters ◽  
Dynamic Information ◽  
Adaptive Weight

Based on Lyapunov stability theorem, a common adaptive strategy was designed for a common class of chaotic systems with uncertain parameters. And the discuss on the sign of unknown parameters were avoided because of the adopting of a novel kind of adaptive weight turning law. At last, the convergence time was analyzed to provide a dynamic information for system users

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 Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

2017 ◽  
Vol 7 (6) ◽  
pp. 3446 ◽  
Author(s):  
Hamed Tirandaz ◽  
Mohsen Ahmadnia ◽  
Hamid Reza Tavakoli
Keyword(s):  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Synchronization Problem ◽  
Projective Lag Synchronization ◽  
Control And Synchronization

In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems.

FURTHER RESULTS ON FUNCTIONAL PROJECTIVE SYNCHRONIZATION OF GENESIO–TESI CHAOTIC SYSTEM

2009 ◽  
Vol 23 (15) ◽  
pp. 1889-1895 ◽  
Author(s):  
JU H. PARK
Keyword(s):  
Numerical Simulation ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Feedback Controller ◽  
Projective Synchronization ◽  
Linear Dynamic ◽  
Synchronization Problem ◽  
Control Scheme ◽  
Static Feedback ◽  
Nonlinear Static

This letter considers the functional projective synchronization problem for Genesio–Tesi chaotic systems. Based on our earlier work, a new control scheme, which consists of a linear dynamic controller and a nonlinear static feedback controller, is applied to achieve the synchronization. A numerical simulation is presented to show the usefulness of the proposed control scheme.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

Sign in / Sign up

Export Citation Format

Share Document