SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA LEARNING CONTROL

2005 ◽  
Vol 15 (12) ◽  
pp. 4035-4041 ◽  
Author(s):  
JIAN-XIN XU ◽  
RUI YAN
Keyword(s):  
Chaotic Systems ◽  
Learning Control ◽  
Learning Approach ◽  
Time Varying ◽  
Control Approach ◽  
New Learning ◽  
Time Varying Parameters ◽  
Uncertain Chaotic Systems ◽  
Time Invariant ◽  
Asymptotic Synchronization

In this paper, a learning control approach is applied to the synchronization of two uncertain chaotic systems which contain both time varying and time invariant parametric uncertainties. The new learning approach also deals with unknown time varying parameters having distinct periods in the master and slave systems. Using the Lyapunov–Krasovskii functional and incorporating periodic parametric learning mechanism, the global stability and asymptotic synchronization between the master and the slave systems are obtained. Simulations on a representative class of chaotic systems show the effectiveness of the method.

EXPLOITING SYNCHRONIZATION TO COMBAT CHANNEL DISTORTIONS IN COMMUNICATION WITH CHAOTIC SYSTEMS

2000 ◽  
Vol 10 (04) ◽  
pp. 777-785
Author(s):  
NARESH SHARMA ◽  
EDWARD OTT
Keyword(s):  
Chaotic Systems ◽  
Additive Noise ◽  
Time Varying ◽  
Linear Filtering ◽  
Order Unity ◽  
Noise Estimate ◽  
Successful Recovery ◽  
Time Varying Parameters ◽  
Transmitted Signal ◽  
Time Invariant

We propose and illustrate a synchronization-based method to combat the channel distortions of a signal transmitted by a chaos-based communication system. In particular, we consider channel distortions like time-varying fading, multipath and time-invariant linear filtering and additive noise. The time-varying parameters are tracked at the receiver to maintain synchronization. The correct noise estimate at the receiver yields synchronization and has minimum norm. A numerical experiment illustrating the method is presented, and shows that successful recovery of the transmitted signal is possible for signal to noise ratios of order unity.

scholarly journals Adaptive hybrid function projective synchronization of chaotic systems with fully unknown periodical time-varying parameters

2019 ◽  
Vol 18 (1) ◽  
pp. 112-128
Author(s):  
Jinsheng Xing
Keyword(s):  
Adaptive Learning ◽  
Chaotic Systems ◽  
Learning Control ◽  
Projective Synchronization ◽  
Time Varying ◽  
Hybrid Functional ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Adaptive Learning Control ◽  
Different Chaotic Systems

In this paper, an adaptive learning control approach is presented for the hybrid functional projective synchronization (HFPS) of different chaotic systems with fully unknown periodical time-varying parameters. Differential-difference hybrid parametric learning laws and an adaptive learning control law are constructed via the Lyapunov–Krasovskii functional stability theory, which make the states of two different chaotic systems asymptotically synchronized in the sense of mean square norm. Moreover, the boundedness of the parameter estimates are also obtained. The Lorenz system and Chen system are illustrated to show the effectiveness of the hybrid functional projective synchronization scheme.

Synchronization of Chaotic Systems with Uncertain Time-Varying Parameters

2015 ◽  
Vol 9 (6) ◽  
pp. 568
Author(s):  
Ahmad Al-Jarrah ◽  
Mohammad Ababneh ◽  
Suleiman Bani Hani ◽  
Khalid Al-Widyan
Keyword(s):  
Chaotic Systems ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Uncertain Time

scholarly journals Numerical Study on Identification of Time Varying Parameters of Vibration Systems

1997 ◽  
Vol 4 (1) ◽  
pp. 69-76
Author(s):  
Yanchun Liang ◽  
Qiang Zhen ◽  
Zaishen Wang
Keyword(s):  
Linear Model ◽  
Nonlinear Term ◽  
Numerical Study ◽  
Time Varying ◽  
Linear Vibration ◽  
Factors Affecting ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
On Line ◽  
Time Invariant

An on-line least squares algorithm has previously been successfully applied to linear vibration systems in order to identify time varying parameters. In this article the limitations of the approach and the factors affecting the identification are further examined. The existence of the nonlinear term is determined by means of the time varying characteristics of the estimated linear parameters using the linear model and the data from a time invariant nonlinear system. The identification of the time varying linear parameters is also examined in accordance with the linear model by using the data with nonlinear elements.

Parameter Identification of Time Varying System Using Basic Function Expansion

2011 ◽  
Vol 403-408 ◽  
pp. 2800-2804
Author(s):  
En Wei Chen ◽  
Yi Min Lu ◽  
Zheng Shi Liu ◽  
Yong Wang
Keyword(s):  
High Efficiency ◽  
Moving Average ◽  
Arma Model ◽  
Basic Function ◽  
Least Square ◽  
Autoregressive Moving Average ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Time Invariant

Time-varying parameters identification in linear system is considered, which can be changed into time-invariant coefficient polynomials after Taylor expansion. Using response data to establish the time-varying autoregressive moving average (TV-ARMA) model, then utilizing least-square algorithm to obtain time-invariant coefficients of time-varying parameters. According to error analysis, to reduce errors and improve accuracy, the estimation time is divided into small internals and the above method is used in each interval. Simulation shows that, under certain error condition, the time-varying parameters obtained by the method have good agreement with the theoretical values; the measures taken have strong anti-interference and high efficiency.

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