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.

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.

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.

scholarly journals Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time-Varying Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jinsheng Xing
Keyword(s):  
Chaotic Systems ◽  
Projective Synchronization ◽  
Time Varying ◽  
Chen System ◽  
Varying Parameters ◽  
Function Projective Synchronization ◽  
Time Varying Parameters ◽  
Hybrid Function ◽  
Robust Adaptive ◽  
Different Chaotic Systems

The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time-varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time-varying parameters are bounded by the product of a known function oftand an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage-like adaptation law is also proposed to guarantee the ultimately uni-formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.

scholarly journals SYNCHRONIZATION OF DIFFERENT DIMENSIONAL CHAOTIC SYSTEMS WITH TIME VARYING PARAMETERS, DISTURBANCES AND INPUT NONLINEARITIES

2014 ◽  
Vol 4 (4) ◽  
pp. 323-338
Author(s):  
A. M. A. El-Sayed ◽  
◽  
A. Elsaid ◽  
H. M. Nour ◽  
A. Elsonbaty ◽  
...  
Keyword(s):  
Chaotic Systems ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters

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.

Control of Dynamic Systems With Nonlinearities and Time Varying Parameters

1993 ◽  
Author(s):  
Dirk Söffker ◽  
Peter C. Müller
Keyword(s):  
Dynamic Systems ◽  
Disturbance Rejection ◽  
Linear Time ◽  
Time Varying ◽  
Varying Parameters ◽  
Linear Time Invariant ◽  
Time Variance ◽  
Disturbance Rejection Control ◽  
Time Varying Parameters ◽  
Time Invariant

Abstract The well-known theory of disturbance rejection control and the experience of using a generalized technique with universal fault model for building observers and regulators for the estimation and compensation of disturbances and unmodeled or uncertain effects as well, could be used for controlling dynamic systems with time varying parameters and nonlinearities. Based on a linear time-invariant model the effects of non-linearities and unmodeled dynamics are estimated by an extended observer scheme. Using this information these dynamic effects will be compensated by the developed compensation scheme. Here also different compensation techniques of disturbance rejection control are discussed, compared, and modified. The simulation example of an inverted flexible pendulum shows the efficiency of the method controlling an unstable mechanical system without exact knowledge of structure and parameters of nonlinearity and time-variance.

Modeling of adaptations to physical training by using a recursive least squares algorithm

1997 ◽  
Vol 82 (5) ◽  
pp. 1685-1693 ◽  
Author(s):  
Thierry Busso ◽  
Christian Denis ◽  
Régis Bonnefoy ◽  
André Geyssant ◽  
Jean-René Lacour
Keyword(s):  
Least Squares ◽  
Physical Training ◽  
Recursive Least Squares ◽  
Model Parameters ◽  
Time Varying ◽  
Varying Parameters ◽  
Recursive Least Squares Algorithm ◽  
Time Varying Parameters ◽  
Least Squares Algorithm ◽  
Time Invariant

Busso, Thierry, Christian Denis, Régis Bonnefoy, André Geyssant, and Jean-René Lacour. Modeling of adaptations to physical training by using a recursive least squares algorithm. J. Appl. Physiol. 82(5): 1685–1693, 1997.—The present study assesses the usefulness of a systems model with time-varying parameters for describing the responses of physical performance to training. Data for two subjects who undertook a 14-wk training on a cycle ergometer were used to test the proposed model, and the results were compared with a model with time-invariant parameters. Two 4-wk periods of intensive training were separated by a 2-wk period of reduced training and followed by a 4-wk period of reduced training. The systems input ascribed to the training doses was made up of interval exercises and computed in arbitrary units. The systems output was evaluated one to five times per week by using the endurance time at a constant workload. The time-invariant parameters were fitted from actual performances by using the least squares method. The time-varying parameters were fitted by using a recursive least squares algorithm. The coefficients of determination r 2 were 0.875 and 0.879 for the two subjects using the time-varying model, higher than the values of 0.682 and 0.666, respectively, obtained with the time-invariant model. The variations over time in the model parameters resulting from the expected reduction in the residuals appeared generally to account for changes in responses to training. Such a model would be useful for investigating the underlying mechanisms of adaptation and fatigue.

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