Chaos synchronization of a fractional-order modified Van der Pol-Duffing system via new linear control, backstepping control and Takagi-Sugeno fuzzy approaches

Complexity ◽  
2015 ◽  
Vol 21 (S1) ◽  
pp. 116-124 ◽  
Author(s):  
Ahmed Ezzat Matouk
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Backstepping Control ◽  
Linear Control ◽  
Van Der Pol ◽  
Duffing System ◽  
Takagi Sugeno

scholarly journals SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

2010 ◽  
Vol 20 (01) ◽  
pp. 81-97 ◽  
Author(s):  
ZAID M. ODIBAT ◽  
NATHALIE CORSON ◽  
M. A. AZIZ-ALAOUI ◽  
CYRILLE BERTELLE
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Dynamics ◽  
Sufficient Conditions ◽  
Linear Control ◽  
Fractional Order Systems ◽  
Control Laws ◽  
Response System ◽  
The Stability ◽  
Stability Results

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

Synchronization in Integer and Fractional Order Chaotic Systems

2011 ◽  
pp. 127-151
Author(s):  
Ahmed E. Matouk
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Fractional Order Systems ◽  
Chen System ◽  
Van Der Pol ◽  
Coupling Technique ◽  
The Laplace Transform

In this chapter, the author introduces the basic methods of chaos synchronization in integer order systems, such as Pecora and Carroll method and One-Way coupling technique, applying these synchronization methods to the modified autonomous Duffing-Van der Pol system (MADVP). The conditional Lyapunov exponents (CLEs) are also calculated for the drive and response MADVP systems which match with the analytical results given by Pecora and Carroll method. Based on Lyapunov stability theory, chaos synchronization is achieved for two coupled MADVP systems by finding a suitable Lyapunov function. Moreover, synchronization in fractional order chaotic systems is also introduced. The conditions of Pecora and Carroll method and One-Way coupling method in fractional order systems are also investigated. In addition, chaos synchronization is achieved for two coupled fractional order MADVP systems using One-Way coupling technique. Furthermore, synchronization between two different fractional order chaotic systems is studied; the fractional order Lü system is controlled to be the fractional order Chen system. The analytical conditions for the synchronization of this pair of different fractional order chaotic systems are derived by utilizing the Laplace transform theory. Numerical simulations are carried out to show the effectiveness of all the proposed synchronization techniques.

scholarly journals Design of PDC Controllers by Matrix Reversibility for Synchronization ofYinandYangChaotic Takagi-Sugeno Fuzzy Henon Maps

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Chun-Yen Ho ◽  
Hsien-Keng Chen ◽  
Zheng-Ming Ge
Keyword(s):  
Chaos Synchronization ◽  
Matrix Theory ◽  
Chinese Philosophy ◽  
Fuzzy Model ◽  
Invertible Matrix ◽  
Henon Maps ◽  
Hénon Maps ◽  
Feminine Principle ◽  
Simulation Results ◽  
Takagi Sugeno

This paper investigates the synchronization ofYinandYangchaotic T-S fuzzy Henon maps via PDC controllers. Based on the Chinese philosophy,Yinis the decreasing, negative, historical, or feminine principle in nature, whileYangis the increasing, positive, contemporary, or masculine principle in nature.YinandYangare two fundamental opposites in Chinese philosophy. The Henon map is an invertible map; so the Henon maps with increasing and decreasing argument can be called theYangandYinHenon maps, respectively. Chaos synchronization ofYinandYangT-S fuzzy Henon maps is achieved by PDC controllers. The design of PDC controllers is based on the linear invertible matrix theory. The T-S fuzzy model ofYinandYangHenon maps and the design of PDC controllers are novel, and the simulation results show that the approach is effective.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

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