Application to Chaos Control and Chaos Synchronization

2008 ◽  
pp. 337-369
Keyword(s):  
Chaos Synchronization ◽  
Chaos Control

scholarly journals Qualitative Study of a 4D Chaos Financial System

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Fuchen Zhang ◽  
Gaoxiang Yang ◽  
Yong Zhang ◽  
Xiaofeng Liao ◽  
Guangyun Zhang
Keyword(s):  
Hausdorff Dimension ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Dynamical Behavior ◽  
Lyapunov Stability Theory ◽  
Attraction Domain ◽  
Ultimate Boundedness ◽  
Lyapunov Dimension ◽  
Simulation Results ◽  
Ultimate Bound

Some dynamics of a new 4D chaotic system describing the dynamical behavior of the finance are considered. Ultimate boundedness and global attraction domain are obtained according to Lyapunov stability theory. These results are useful in estimating the Lyapunov dimension of attractors, Hausdorff dimension of attractors, chaos control, and chaos synchronization. We will also present some simulation results. Furthermore, the volumes of the ultimate bound set and the global exponential attractive set are obtained.

A hyperchaotic memristor oscillator with fuzzy based chaos control and LQR based chaos synchronization

2018 ◽  
Vol 94 ◽  
pp. 55-68 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Hadi Jahanshahi ◽  
Metin Varan ◽  
Ihsan Bayır ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Chaos Synchronization ◽  
Chaos Control

GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE LORENZ SYSTEM

2006 ◽  
Vol 16 (03) ◽  
pp. 757-764 ◽  
Author(s):  
PEI YU ◽  
XIAOXIN LIAO
Keyword(s):  
Lyapunov Function ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Lorenz System ◽  
Equilibrium Points ◽  
Invariant Set ◽  
The Lorenz System ◽  
Globally Attractive ◽  
Generalized Lyapunov Function ◽  
Positive Invariant Set

In this paper, based on a generalized Lyapunov function, a simple proof is given to improve the estimation of globally attractive and positive invariant set of the Lorenz system. In particular, a new estimation is derived for the variable x. On the globally attractive set, the Lorenz system satisfies Lipschitz condition, which is very useful in the study of chaos control and chaos synchronization. Applications are presented for globally, exponentially tracking periodic solutions, stabilizing equilibrium points and synchronizing two Lorenz systems.

scholarly journals Adaptive Control and Synchronization of the Shallow Water Model

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
P. Sangapate
Keyword(s):  
Adaptive Control ◽  
Shallow Water ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Sufficient Conditions ◽  
Water Model ◽  
Shallow Water Model ◽  
Control Laws ◽  
Barbalat’S Lemma ◽  
Control And Synchronization

The shallow water model is one of the important models in dynamical systems. This paper investigates the adaptive chaos control and synchronization of the shallow water model. First, adaptive control laws are designed to stabilize the shallow water model. Then adaptive control laws are derived to chaos synchronization of the shallow water model. The sufficient conditions for the adaptive control and synchronization have been analyzed theoretically, and the results are proved using a Barbalat's Lemma.

Chaos control and chaos synchronization using the state-dependent Riccati equation techniques

2018 ◽  
Vol 41 (2) ◽  
pp. 311-320 ◽  
Author(s):  
Yazdan Batmani
Keyword(s):  
Riccati Equation ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Design Procedure ◽  
The State ◽  
Suboptimal Control ◽  
Control Law ◽  
Closed Loop System ◽  
Infinite Time ◽  
State Dependent

In this paper, the problems of chaos control and chaos synchronization are solved using the state-dependent Riccati equation methods. In the former problem, a nonlinear suboptimal control law is found, which leads to a stable closed-loop system. In the latter, an optimal infinite-time horizon tracking problem is defined and solved using the state-dependent Riccati equation technique. It is shown that the synchronization error between the slave and the master systems converges asymptotically to zero under some mild conditions. Three numerical simulations are provided to demonstrate the design procedure and the flexibility of the methods.

Chaos, chaos control and synchronization of the vibrometer system

2004 ◽  
Vol 218 (9) ◽  
pp. 1001-1020 ◽  
Author(s):  
Z-M Ge ◽  
C-C Lin ◽  
Y-S Chen
Keyword(s):  
Feedback Control ◽  
Numerical Methods ◽  
Dynamic System ◽  
Chaos Synchronization ◽  
Chaos Control ◽  
Chaotic Behaviour ◽  
Chaotic Motions ◽  
Control And Synchronization

The dynamic system of the vibrometer is shown to produce regular and chaotic behaviour as the parameters are varied. When the system is non-autonomous, the periodic and chaotic motions are obtained by numerical methods. Many effective methods have been used in chaos synchronization. It has been shown that chaos can be synchronized using special feedback control and that external excitations affect the synchronization.

ON THE RELATIONSHIP BETWEEN PARAMETRIC VARIATION AND STATE FEEDBACK IN CHAOS CONTROL

2002 ◽  
Vol 12 (06) ◽  
pp. 1411-1415 ◽  
Author(s):  
ZENGRONG LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaos Synchronization ◽  
State Feedback ◽  
Chaos Control ◽  
Point Of View ◽  
Form Analysis ◽  
Parametric Variation ◽  
Potential Applications ◽  
New Perspective ◽  
First Time ◽  
The Relationship

In this Letter, we study the popular parametric variation chaos control and state-feedback methodologies in chaos control, and point out for the first time that they are actually equivalent in the sense that there exist diffeomorphisms that can convert one to the other for most smooth chaotic systems. Detailed conversions are worked out for typical discrete chaotic maps (logistic, Hénon) and continuous flows (Rösller, Lorenz) for illustration. This unifies the two seemingly different approaches from the physics and the engineering communities on chaos control. This new perspective reveals some new potential applications such as chaos synchronization and normal form analysis from a unified mathematical point of view.

Sign in / Sign up

Export Citation Format

Share Document