scholarly journals Adaptive Feedback Control for Chaos Control and Synchronization for New Chaotic Dynamical System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
M. M. El-Dessoky ◽  
M. T. Yassen
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Feedback Control ◽  
Chaos Control ◽  
Control Technique ◽  
Unknown Parameters ◽  
Chaotic Dynamical System ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Control And Synchronization

This paper investigates the problem of chaos control and synchronization for new chaotic dynamical system and proposes a simple adaptive feedback control method for chaos control and synchronization under a reasonable assumption. In comparison with previous methods, the present control technique is simple both in the form of the controller and its application. Based on Lyapunov's stability theory, adaptive control law is derived such that the trajectory of the new system with unknown parameters is globally stabilized to the origin. In addition, an adaptive control approach is proposed to make the states of two identical systems with unknown parameters asymptotically synchronized. Numerical simulations are shown to verify the analytical results.

A study of a modified nonlinear dynamical system with fractal-fractional derivative

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sunil Kumar ◽  
R.P. Chauhan ◽  
Shaher Momani ◽  
Samir Hadid
Keyword(s):  
Dynamical System ◽  
Fractional Derivative ◽  
Active Control ◽  
Numerical Scheme ◽  
Chaos Control ◽  
Nonlinear Dynamical System ◽  
Control Technique ◽  
Complex Behavior ◽  
Content Type ◽  
Control And Synchronization

Purpose This paper aims to study the complex behavior of a dynamical system using fractional and fractal-fractional (FF) derivative operators. The non-classical derivatives are extremely useful for investigating the hidden behavior of the systems. The Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) derivatives are considered for the fractional structure of the model. Further, to add more complexity, the authors have taken the system with a CF fractal-fractional derivative having an exponential kernel. The active control technique is also considered for chaos control. Design/methodology/approach The systems under consideration are solved numerically. The authors show the Adams-type predictor-corrector scheme for the AB model and the Adams–Bashforth scheme for the CF model. The convergence and stability results are given for the numerical scheme. A numerical scheme for the FF model is also presented. Further, an active control scheme is used for chaos control and synchronization of the systems. Findings Simulations of the obtained solutions are displayed via graphics. The proposed system exhibits a very complex phenomenon known as chaos. The importance of the fractional and fractal order can be seen in the presented graphics. Furthermore, chaos control and synchronization between two identical fractional-order systems are achieved. Originality/value This paper mentioned the complex behavior of a dynamical system with fractional and fractal-fractional operators. Chaos control and synchronization using active control are also described.

H_Infinity Anti-Synchronization of Chaotic Systems with Unknown Parameters

2013 ◽  
Vol 336-338 ◽  
pp. 528-531 ◽  
Author(s):  
Li Ming Du ◽  
Feng Ying Wang ◽  
Hui Zhang
Keyword(s):  
Adaptive Control ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Chaotic Systems ◽  
External Disturbance ◽  
Unknown Parameters ◽  
Adaptive Feedback ◽  
Lyapunov Control ◽  
Norm Constraint ◽  
General Method

In this paper, a general method is proposed for the anti-synchronization of chaotic systems with unknown parameters. This approach is based on the Lyapunov control theory, and employs a combination of feedback control and adaptive control. With this method, the unknown parameters is estimated and the adaptive feedback controller is designed to not only guarantee stable anti-synchronization but also reduce the effect of external disturbance to an norm constraint. Numerical simulations results are presented to demonstrate the effectiveness of the method.

scholarly journals Adaptive Control and Synchronization of Sprott J System With Estimation Of Fully Unknown Parameters

2015 ◽  
Vol 45 (2) ◽  
pp. 45-58 ◽  
Author(s):  
Mitul Islam ◽  
Nurul Islam ◽  
Svetoslav Nikolov
Keyword(s):  
Dynamical System ◽  
Adaptive Control ◽  
Lyapunov Function ◽  
Numerical Simulations ◽  
Unknown Parameters ◽  
Adaptive Scheme ◽  
System A ◽  
Control And Synchronization ◽  
Synchronization Scheme ◽  
Derivatives Of

Abstract This communication develops an adaptive scheme for control and synchronization of Sprott J system with fully unknown parameters. The scheme provides an elegant strategy of designing estimators for identification of the unknown parameters of the underlying dynamical system. Adaptive control and update laws are proposed to globally stabilize the chaotic Sprott J system. A pair of identical Sprott J systems with un- known parameters are globally synchronized with the help of adaptive control and parameter update laws. The results are established using LaSalle invariance principle, which lays down weaker restrictions on the derivatives of the Lyapunov function, and producing more general results. All the results obtained in the paper are global in nature. Numerical simulations are performed to illustrate the validity and effectiveness of the proposed adaptive control and synchronization scheme in the context of the Sprott J system. The parameter identification capability of the scheme is also explored.

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