Controlling chaos and synchronization for new chaotic system using linear feedback control

Yassen, M.T.

doi:10.1016/j.chaos.2005.01.047

Cited by 166 publications

(83 citation statements)

References 14 publications

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“…In recent years, dynamical behavior and chaos synchronization of certain special cases of (1.1) have been studied, see, e.g. [9][10][11][12]. Several methods have been introduced and applied to study chaos synchronization of chaotic nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

2007

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In this paper, we introduce a new chaotic complex nonlinear system and study its dynamical properties including invariance, dissipativity, equilibria and their stability, Lyapunov exponents, chaotic behavior, chaotic attractors, as well as necessary conditions for this system to generate chaos. Our system displays 2 and 4-scroll chaotic attractors for certain values of its parameters. Chaos synchronization of these attractors is studied via active control and explicit expressions are derived for the control functions which are used to achieve chaos synchronization. These expressions are tested numerically and excellent agreement is found. A Lyapunov function is derived to prove that the error system is asymptotically stable.

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Section: Introductionmentioning

confidence: 99%

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

2007

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“…Active synchronization problem of two chaotic systems with known parameters are vastly investigated by the researchers. For example, in [5,3,35], the active controlling method is studied for synchronization of two typical chaotic systems. And also, in [2], an active method for controling the behavior of a unified chaotic system is presented.…”

Section: Introductionmentioning

confidence: 99%

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

Tirandaz

Ahmadnia

Tavakoli

2017

IJECE

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The synchronization problem of chaotic systems using active modified projective nonlinear control method is rarely addressed. Thus the concentration of this study is to derive a modified projective controller to synchronize the two chaotic systems. Since, the parameter of the master and follower systems are considered known, so active methods are employed instead of adaptive methods. The validity of the proposed controller is studied by means of the Lyapunov stability theorem. Furthermore, some numerical simulations are shown to verify the validity of the theoretical discussions. The results demonstrate the effectiveness of the proposed method in both speed and accuracy points of views.Copyright c 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Hamed Tirandaz Hakim Sabzevari University Electrical and Computer Engineering Faculty, Hakim Sabzevari University, Sabzevar, Iran. Phone +98051-4401288 Email: tirandaz@hsu.ac.ir INTRODUCTIONMaster-slave synchronization of chaotic systems is strikely nonlinear, since the aperiodic and nonregular behavior of chaotic systems and their sensitivity to the initial conditions. Chaotic behavior may appear in many physical systems. So, chaos synchronization subject has received a great deal of attention in the last to decades, due to its potential applications in physics, chemistry, electrical engineering, secure communication and so on [1]. Up to now, many types of controling methods are revealed and investigated for control and synchronization of chaotic systems. Active method [2,3,4,5,6], adaptive method [7,8,9] [22,23,24] are some of the introduced methods by the researchers. Among these methods, synchronization with some types of projective methods are extensively investigated in the last decades, since the faster synchronization due to its synchronization scaling factors, which master and slave chaotic systems would be synchronized up to a proportional rate. Projective lag method [25], modified projective synchronization (MPS) [26,27,28], function projective synchronization (FPS) [29], modified function projective synchronization [30,28], generalized function projective synchronization [31,32] and modified projective lag synchronization [33,34] are some generalized schemes of projective method, which utilize some type of scaling factors.When the parameters of a chaotic system are known beforehand, active related methods are preferably chosen than adaptive methods. Active synchronization problem of two chaotic systems with known parameters are vastly investigated by the researchers. For example, in [5,3,35], the active controlling method is studied for synchronization of two typical chaotic systems. And also, in [2], an active method for controling the behavior of a unified chaotic system is presented. Chaos synchronization of complex Chen and Lu chaotic systems are addressed in citeMahmoud, with designing an active control method. Furthermore, in [36] active

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“…13 Chaos, its control and synchronization for a fractional-order rotational machine system with a centrifugal governor is investigated. 5 Moreover, the OGY method, 14 linear and nonlinear feedback control, 15,16 adaptive method 17 and time-delay feedback control 18 are considered as the efficient tools for controlling chaotic oscillation. However, precision model and accurate parameters are the prerequisite in the process of design and the states trajectories of the system can converge to zero when time is tending towards infinity.…”

Section: Introductionmentioning

confidence: 99%

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

2016

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This paper addresses chaos suppression of the mechanical centrifugal flywheel governor system with output constraint and fully unknown parameters via adaptive dynamic surface control. To have a certain understanding of chaotic nature of the mechanical centrifugal flywheel governor system and subsequently design its controller, the useful tools like the phase diagrams and corresponding time histories are employed. By using tangent barrier Lyapunov function, a dynamic surface control scheme with neural network and tracking differentiator is developed to transform chaos oscillation into regular motion and the output constraint rule is not broken in whole process. Plugging second-order tracking differentiator into chaos controller tackles the “explosion of complexity” of backstepping and improves the accuracy in contrast with the first-order filter. Meanwhile, Chebyshev neural network with adaptive law whose input only depends on a subset of Chebyshev polynomials is derived to learn the behavior of unknown dynamics. The boundedness of all signals of the closed-loop system is verified in stability analysis. Finally, the results of numerical simulations illustrate effectiveness and exhibit the superior performance of the proposed scheme by comparing with the existing ADSC method.

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Controlling chaos and synchronization for new chaotic system using linear feedback control

Cited by 166 publications

References 14 publications

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system

Modified Projective Synchronization of Chaotic Systems with Noise Disturbance, an Active Nonlinear Control Method

Performance enhanced design of chaos controller for the mechanical centrifugal flywheel governor system via adaptive dynamic surface control

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