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.

Fuzzy Adaptive Output Tracking Controller for a Class of Chaotic Systems

2012 ◽  
Vol 488-489 ◽  
pp. 1793-1797
Author(s):  
R. Ghasemi ◽  
M.B. Menhaj ◽  
B. Abdi
Keyword(s):  
Chaotic Systems ◽  
Closed Loop ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
External Disturbances ◽  
Output Tracking ◽  
Fuzzy Adaptive Controller ◽  
Simulation Results ◽  
The Stability ◽  
Fuzzy Adaptive

This paper proposes a new method for designing a fuzzy adaptive controller for a class of non-affine nonlinear chaotic systems in which functions of the systems are unknown. The proposed method is aimed on a class of non-canonical non-affine nonlinear chaotic systems. The stability of the closed loop system is guaranteed based on Lyapunov’s theory. The proposed controller is robust against uncertainties and external disturbances. The simulation results show the effectiveness of the proposed method.

Fuzzy Control-Based Synchronization of Fractional-Order Chaotic Systems With Input Nonlinearities

2018 ◽  
pp. 261-288 ◽  
Author(s):  
Abdesselem Boulkroune ◽  
Amina Boubellouta
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Controller Design ◽  
Variable Structure ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Fuzzy Logic Systems ◽  
Bounded Disturbances ◽  
The Stability ◽  
Fuzzy Adaptive

This chapter addresses the fuzzy adaptive controller design for the generalized projective synchronization (GPS) of incommensurate fractional-order chaotic systems with actuator nonlinearities. The considered master-slave systems are with different fractional-orders, uncertain models, unknown bounded disturbances, and non-identical form. The suggested controller includes two keys terms, namely a fuzzy adaptive control and a fractional-order variable structure control. The fuzzy logic systems are exploited for approximating the system uncertainties. A Lyapunov approach is employed for determining the parameter adaptation laws and proving the stability of the closed-loop system. At last, simulation results are given to demonstrate the validity of the proposed synchronization approach.

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.

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Hadi Delavari ◽  
Milad Mohadeszadeh
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adaptive Controller ◽  
Projective Synchronization ◽  
Order Complex ◽  
Unknown Parameters ◽  
Adaptive Sliding Mode Controller ◽  
Robust Adaptive ◽  
Complex Chaotic Systems

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

scholarly journals Synchronization of Different Uncertain Fractional-Order Chaotic Systems with External Disturbances via T-S Fuzzy Model

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Lin Wang ◽  
Jinbo Ni ◽  
Chunzhi Yang
Keyword(s):  
Fractional Order ◽  
Fuzzy Systems ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Fuzzy Model ◽  
Adaptive Controller ◽  
Lyapunov Theory ◽  
System Structure ◽  
External Disturbances ◽  
Hyperchaotic Systems

This paper presents an adaptive fuzzy synchronization control strategy for a class of different uncertain fractional-order chaotic/hyperchaotic systems with unknown external disturbances via T-S fuzzy systems, where the parallel distributed compensation technology is provided to design adaptive controller with fractional adaptation laws. T-S fuzzy models are employed to approximate the unknown nonlinear systems and tracking error signals are used to update the parametric estimates. The asymptotic stability of the closed-loop system and the boundedness of the states and parameters are guaranteed by fractional Lyapunov theory. This approach is also valid for synchronization of fractional-order chaotic systems with the same system structure. One constructive example is given to verify the feasibility and superiority of the proposed method.

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