scholarly journals Model Reference Control of Hyperchaotic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Pengfei Zhao ◽  
Cai Liu ◽  
Xuan Feng
Keyword(s):  
Lyapunov Stability ◽  
Reference System ◽  
Stability Theorem ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
General Description ◽  
Lyapunov Stability Theorem ◽  
Model Reference ◽  
Model Reference Control ◽  
Hyperchaotic Systems

We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for controlling hyperchaotic systems with both certain parameters and uncertain parameters.

GENERALIZED PROJECTIVE SYNCHRONIZATION AND PARAMETERS ESTIMATION OF TWO NEW HYPERCHAOTIC SYSTEMS WITH FULLY UNCERTAIN PARAMETERS

2010 ◽  
Vol 21 (02) ◽  
pp. 249-259 ◽  
Author(s):  
CONG-XU ZHU
Keyword(s):  
Adaptive Control ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Parameters Estimation ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems ◽  
Theoretical Results

This paper investigates adaptive generalized projective synchronization (GPS) between two novel hyperchaotic systems with different structure and fully uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, GPS between the two hyperchaotic systems is achieved by proposing a new adaptive controller and a novel parameters estimation update law. Strict theoretical proof is put forward. Numerical simulations are presented to demonstrate the effectiveness of the proposed GPS scheme and verify 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

ADAPTIVE SYNCHRONIZATION OF A NOVEL HYPERCHAOTIC SYSTEM WITH FULLY UNKNOWN PARAMETERS

2013 ◽  
Vol 27 (32) ◽  
pp. 1350197
Author(s):  
XING-YUAN WANG ◽  
SI-HUI JIANG ◽  
CHAO LUO
Keyword(s):  
Lyapunov Stability ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Chaotic Synchronization ◽  
Adaptive Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Chen System ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

In this paper, a chaotic synchronization scheme is proposed to achieve adaptive synchronization between a novel hyperchaotic system and the hyperchaotic Chen system with fully unknown parameters. Based on the Lyapunov stability theory, an adaptive controller and parameter updating law are presented to synchronize the above two hyperchaotic systems. The corresponding theoretical proof is given and numerical simulations are presented to verify the effectiveness of the proposed scheme.

ANTI-SYNCHRONIZATION OF A CLASS OF COUPLED CHAOTIC SYSTEMS VIA LINEAR FEEDBACK CONTROL

2006 ◽  
Vol 16 (04) ◽  
pp. 1041-1047 ◽  
Author(s):  
CHUANDONG LI ◽  
XIAOFENG LIAO
Keyword(s):  
Lyapunov Stability ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Feedback ◽  
Generalized Synchronization ◽  
Lyapunov Stability Theorem ◽  
Linear Feedback Control ◽  
Relevant Variables ◽  
Special Case

As a special case of generalized synchronization, chaos anti-synchronization can be characterized by the vanishing of the sum of relevant variables. In this paper, based on Lyapunov stability theorem for ordinary differential equations, several sufficient conditions for guaranteeing the existence of anti-synchronization in a class of coupled identical chaotic systems via linear feedback or adaptive linear feedback methods are derived. Chua's circuit is presented as an example to demonstrate the effectiveness of the proposed approach by computer simulations.

scholarly journals Lyapunov Stability Analysis of Gradient Descent-Learning Algorithm in Network Training

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Ahmad Banakar
Keyword(s):  
Lyapunov Stability ◽  
Gradient Descent ◽  
Learning Algorithm ◽  
Stability Theorem ◽  
Stability And Convergence ◽  
Lyapunov Stability Theorem ◽  
Network Training ◽  
Learning Rates ◽  
Lyapunov Stability Analysis ◽  
The Stability

The Lyapunov stability theorem is applied to guarantee the convergence and stability of the learning algorithm for several networks. Gradient descent learning algorithm and its developed algorithms are one of the most useful learning algorithms in developing the networks. To guarantee the stability and convergence of the learning process, the upper bound of the learning rates should be investigated. Here, the Lyapunov stability theorem was developed and applied to several networks in order to guaranty the stability of the learning 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.

scholarly journals Adaptive Multi-Switching Synchronization of High-Order Memristor-Based Hyperchaotic System with Unknown Parameters and Its Application in Secure Communication

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Zhili Xiong ◽  
Shaocheng Qu ◽  
Jing Luo
Keyword(s):  
Numerical Simulation ◽  
Secure Communication ◽  
High Order ◽  
Hyperchaotic System ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Switching Controller ◽  
Simulation Results ◽  
Hyperchaotic Systems ◽  
True Values

This article investigates an adaptive multi-switching synchronization for two identical high-order memristor-based hyperchaotic systems with uncertain parameters. Firstly, the dynamic characteristics of two high-order memristor hyperchaotic systems with uncertain parameters are analyzed. Then, an adaptive multi-switching controller is designed to realize the multi-switching synchronization of the two high-order hyperchaotic systems, and the unknown parameters of the systems are identified to their true values. Furthermore, numerical simulation results testify the effectiveness of the proposed strategy. Finally, the proposed algorithm applied in secure communication of masking encryption and image encryption is validated by statistical analysis.

Sign in / Sign up

Export Citation Format

Share Document