Backstepping Control for Combined Function Projective Synchronization Among Fractional Order Chaotic Systems with Uncertainties and External Disturbances

2018 ◽  
pp. 115-132 ◽  
Author(s):  
Vijay K. Yadav ◽  
Mayank Srivastava ◽  
Subir Das
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Backstepping Control ◽  
Projective Synchronization ◽  
External Disturbances ◽  
Function Projective Synchronization

Fuzzy Adaptive Controller for Synchronization of Uncertain Fractional-Order Chaotic Systems

2018 ◽  
pp. 190-217 ◽  
Author(s):  
Amel Bouzeriba
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
External Disturbances ◽  
Fuzzy Approximation ◽  
Adaptive Laws ◽  
Adaptive Fuzzy Logic ◽  
Fuzzy Adaptive Controller ◽  
Fuzzy Adaptive

In this chapter, the projective synchronization problem of different multivariable fractional-order chaotic systems with both uncertain dynamics and external disturbances is studied. More specifically, a fuzzy adaptive controller is investigated for achieving a projective synchronization of uncertain fractional-order chaotic systems. The adaptive fuzzy-logic system is used to online estimate the uncertain nonlinear functions. The latter is augmented by a robust control term to efficiently compensate for the unavoidable fuzzy approximation errors, external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is employed to derive the parameter adaptation laws and to prove the boundedness of all signals of the closed-loop system. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.

scholarly journals A Novel Hybrid Function Projective Synchronization between Different Fractional-Order Chaotic Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Ping Zhou ◽  
Xiao-You Yang
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Scaling Function ◽  
Uncertain System ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Response System ◽  
Parameter Update Law ◽  
Hybrid Function

An adaptive hybrid function projective synchronization (AHFPS) scheme between different fractional-order chaotic systems with uncertain system parameter is addressed in this paper. In this proposed scheme, the drive and response system could be synchronized up to a vector function factor. This proposed scheme is different with the function projective synchronization (FPS) scheme, in which the drive and response system could be synchronized up to a scaling function factor. The adaptive controller and the parameter update law are gained. Two examples are presented to demonstrate the effectiveness of the proposed scheme.

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