Generalized projective synchronization of Elhadj chaotic systems via adaptive control

Vaidyanathan, Sundarapandian; Pakiriswamy, Sarasu

doi:10.1109/icgce.2013.6823509

Cited by 5 publications

(4 citation statements)

References 36 publications

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“…So far many types of projective methods have been studied by the researchers. Modified projective synchronization (MPS) [21]- [24], function projective synchronization (FPS) [25], [26], modified function projective synchronization (MFPS) [27], generalized function projective synchronization [28]- [30] are some of the projective related method for control and synchronization between two identical/non-identical chaotic systems. But, projective lag hybrid synchronization is rarely investigated by the researchers.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

Tirandaz¹,

Ahmadnia²,

Tavakoli³

2017

IJECE

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In this paper, the synchronization problem of T chaotic system and Lu chaotic system is studied. The parameter of the drive T chaotic system is considered unknown. An adaptive projective lag control method and also parameter estimation law are designed to achieve chaos synchronization problem between two chaotic systems. Then Lyapunov stability theorem is utilized to prove the validity of the proposed control method. After that, some numerical simulations are performed to assess the performance of the proposed method. The results show high accuracy of the proposed method in control and synchronization of chaotic systems. Keyword:Adaptive method Lyapunov stability theorem Chaos synchronization Projective lag method Copyright © 2017 Institute of Advanced Engineering and Science.All rights reserved. Corresponding Author:Hamed Tirandaz, Electrical and Computer Engineering Department, Hakim Sabzevari University, Sabzevar, Iran. Email: tirandaz@hsu.ac.ir INTRODUCTIONSensitivity to the initial values of the state variables is the main feature of any chaotic system, which causes exponentially different motion trajectories of the state variables with different initial conditions. The problem of chaos synchronization has received a lot of attention in the last three decades due to its potential applications in many different fields such as: physics, chemistry, electrical engineering, economics and secure communications. Until now, many kind of chaos control and synchronization schemes have developed by the researchers. [20] are some of the investigated method during the last recent years. Among these investigated methods, chaos synchronization related to the projective method has considerably noticed during the last few decades due to its proportional feature, which the response chaotic system can be synchronized up to a typical aligned scaling factors. So far many types of projective methods have been studied by the researchers. [30] are some of the projective related method for control and synchronization between two identical/non-identical chaotic systems. But, projective lag hybrid synchronization is rarely investigated by the researchers. So, this paper is devoted to the synchronization problem between T chaotic system and Lorenz chaotic system by designing an appropriate adaptive hybrid projective lag synchronization method.The rest reminder of this paper is constructed as follows: In Section 2, the structure of the T chaotic system and Lorenz chaotic system are described. Then, in Section 3, the problem of chaos synchronization of T chaotic system and Lorenz chaotic system is given. An adaptive projective lag control method is designed

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Section: Introductionmentioning

confidence: 99%

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

Tirandaz¹,

Ahmadnia²,

Tavakoli³

2017

IJECE

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“…Chaos theory has applications in several fields of science and engineering such as oscillators [47,48,49,50,51,52,53,54,55], dynamos [56,57,58,59], Tokamak systems [60,61], chemical reactions [62,63,64,65,66,67,68,69,70,71], neural networks [72,73,74,75,76,77], neurology [78,79,80,81,82,83], biology [84,85,86,87,88,89,90,91,92], electrical circuits [93,94,95], induction motors [96], cryptosystems …”

Section: Introductionmentioning

confidence: 99%

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

Vaidyanathan

2017

Archives of Control Sciences

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A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control SUNDARAPANDIAN VAIDYANATHAN This paper presents a new seven-term 3-D jerk chaotic system with two cubic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L 1 = 0.2974, L 2 = 0 and L 3 = −3.8974. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the new jerk chaotic system is found as D KY = 2.0763. Next, an adaptive backstepping controller is designed to globally stabilize the new jerk chaotic system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations are shown to illustrate all the main results derived in this work.

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“…Chaos theory has applications in several fields of science and engineering such as oscillators [39,40,41,42,43,44,45,46], dynamos [47,48,49,50], Tokamak systems [51,52], chemical reactions [53,54,55,56,57,58,59,60,61,62], neural networks [63,64,65,66,67,68], neurology [69,70,71,72,73,74], biology [75,76,77,78,79,80,81,82,83], electrical circuits [84,85,86], cryptosystems [87,88], memristors …”

Section: Introductionmentioning

confidence: 99%

A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

Vaidyanathan

2016

Archives of Control Sciences

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A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control SUNDARAPANDIAN VAIDYANATHAN This paper announces an eight-term novel 3-D jerk chaotic system with three quadratic nonlinearities. The phase portraits of the novel jerk chaotic system are displayed and the qualitative properties of the jerk system are described. The novel jerk chaotic system has two equilibrium points, which are saddle-foci and unstable. The Lyapunov exponents of the novel jerk chaotic system are obtained as L 1 = 0.20572, L 2 = 0 and L 3 = −1.20824. Since the sum of the Lyapunov exponents of the jerk chaotic system is negative, we conclude that the chaotic system is dissipative. The Kaplan-Yorke dimension of the novel jerk chaotic system is derived as D KY = 2.17026. Next, an adaptive controller is designed via backstepping control method to globally stabilize the novel jerk chaotic system with unknown parameters. Moreover, an adaptive controller is also designed via backstepping control method to achieve global chaos synchronization of the identical jerk chaotic systems with unknown parameters. The backstepping control method is a recursive procedure that links the choice of a Lyapunov function with the design of a controller and guarantees global asymptotic stability of strict feedback systems. MATLAB simulations have been depicted to illustrate the phase portraits of the novel jerk chaotic system and also the adaptive backstepping control results.

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Generalized projective synchronization of Elhadj chaotic systems via adaptive control

Cited by 5 publications

References 36 publications

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

Adaptive Projective Lag Synchronization of T and Lu Chaotic Systems

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

A novel 3-D jerk chaotic system with three quadratic nonlinearities and its adaptive control

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