Chaos Synchronization in a Class of Chaotic Systems Using Kalman Filter and Feedback Linearization Methods

2006 ◽  
Author(s):  
Hassan Salarieh ◽  
Aria Alasty
Keyword(s):  
Kalman Filter ◽  
Feedback Linearization ◽  
High Performance ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Drive System ◽  
Unknown Parameters ◽  
Linearization Methods ◽  
Filter Approach ◽  
Different Chaotic Systems

In this paper a combination of Kalman filter and feedback linearization methods is used to present a controller-identifier system for synchronizing two different chaotic systems. The drive system has some unknown parameters which are supposed to have linear form within its dynamic equation. An identifier based on Kalman filter approach is designed to estimate the unknown parameters of the drive system, and simultaneously a feedback linearizing controller is used to synchronize the chaotic behavior of the response system with the drive chaotic system. The method proposed in this paper is applied to the Lure’ and the Genesio dynamic systems as the drive and response chaotic systems. The results show the high performance of the method to identify and synchronize two different chaotic systems with unknown parameters and in presence of noise.

FUNCTION PROJECTIVE SYNCHRONIZATION OF THE CHAOTIC SYSTEMS WITH PARAMETERS UNKNOWN

2013 ◽  
Vol 27 (21) ◽  
pp. 1350110
Author(s):  
JIAKUN ZHAO ◽  
YING WU
Keyword(s):  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Hyperchaotic System ◽  
Unknown Parameters ◽  
Function Projective Synchronization ◽  
Parameter Update Law ◽  
Different Chaotic Systems ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

This work is concerned with the general methods for the function projective synchronization (FPS) of chaotic (or hyperchaotic) systems. The aim is to investigate the FPS of different chaotic (hyper-chaotic) systems with unknown parameters. The adaptive control law and the parameter update law are derived to make the states of two different chaotic systems asymptotically synchronized up to a desired scaling function by Lyapunov stability theory. The general approach for FPS of Chen hyperchaotic system and Lü system is provided. Numerical simulations are also presented to verify the effectiveness of the proposed scheme.

ADAPTIVE FUZZY SYNCHRONIZATION OF TWO DIFFERENT CHAOTIC SYSTEMS WITH STOCHASTIC UNKNOWN PARAMETERS

2010 ◽  
Vol 24 (10) ◽  
pp. 979-994 ◽  
Author(s):  
W. J. YOO ◽  
D. H. JI ◽  
S. C. WON
Keyword(s):  
Chaotic Systems ◽  
Adaptive Fuzzy Control ◽  
Nonlinear Function ◽  
Small Error ◽  
Unknown Parameters ◽  
Mean Values ◽  
Adaptive Fuzzy ◽  
Different Chaotic Systems ◽  
Ito's Lemma ◽  
Logic System

In this paper, we present a method for synchronizing two different chaotic systems that have unknown parameters that are affected by stochastic variations generated by the Wiener process. The parameters are expressed by the sum of their mean values and the white Gaussian noise multiplied by the diffusion matrices. To describe the unknown nonlinear function yielded by Itô's lemma due to the unknown diffusion matrices, a fuzzy logic system is employed. Using adaptive fuzzy control, the response system is synchronized with the drive system within an arbitrarily small error bound. Numerical simulations show the effectiveness of the proposed method.

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