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.

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.

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 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

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.

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