Synchronization of an uncertain unified chaotic system via adaptive control

Chen, Shihua; Lü, Jinhu

doi:10.1016/s0960-0779(02)00006-1

Cited by 371 publications

(123 citation statements)

References 9 publications

(11 reference statements)

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“…For the numerical simulations, the fourth-order RungeKutta method with time-step h = 10 −8 is used to solve the two systems of differential equations (19) and (20) with the active nonlinear controller (23).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…We take k i = 4 for i Figure 7 shows the hybrid synchronization of the Wang system (19) and the Liu-Chen system (20). Figure 8 shows the time-history of the hybrid synchronization errors.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Since the seminal work by Pecora and Carroll ( [9], 1990) on complete synchronization of chaotic systems, several approaches have been developed for chaos synchronization such as the OGY method [10], sampled-data feedback synchronization method [11], the time-delay feedback method [12,13], the active control method [14][15][16][17][18], the adaptive control method [19][20][21][22][23], the backstepping method [24][25][26], the sliding mode control method [27][28][29][30] and others.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

Rajagopal¹,

Vaidyanathan

2014

Journal of Electrical Engineering

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This paper investigates the hybrid chaos synchronization of identical Wang four-scroll systems (Wang, 2009), identical Liu-Chen four-scroll systems (Liu and Chen, 2004) and non-identical Wang and Liu-Chen four-scroll systems. Active control method is the method adopted to achieve the hybrid chaos synchronization of the four-scroll chaotic systems addressed in this paper and our synchronization results are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is effective and convenient to hybrid synchronize identical and different Wang and Liu-Chen four-scroll chaotic systems. Numerical simulations are also shown to illustrate and validate the hybrid synchronization results derived in this paper.

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Section: Numerical Resultsmentioning

confidence: 99%

“…We take k i = 4 for i Figure 7 shows the hybrid synchronization of the Wang system (19) and the Liu-Chen system (20). Figure 8 shows the time-history of the hybrid synchronization errors.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control

Rajagopal¹,

Vaidyanathan

2014

Journal of Electrical Engineering

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“…Until now, many kind of chaos control and synchronization schemes have developed by the researchers. Active method [1]- [3], adaptive method [4]- [6], phase method [7], backstepping method [8], [9], lag method [10], impulsive method [11], [12], linear feedback method [13], [14], nonlinear feedback control [15], [16], and projective method [17]- [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.…”

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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“…If a particular chaotic system is called the master or drive system and another chaotic system is called the slave or response system, then the idea of the anti-synchronization is to use the output of the master system to control the slave system so that the states of the slave system have the same amplitude but opposite signs as the states of the master system asymptotically. Since the pioneering work by Pecora and Carroll ( [2], 1990), chaos synchronization problem has been studied extensively and intensively in the literature [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Chaos theory has been applied to a variety of fields such as physical systems [3], chemical systems [4], ecological systems [5], secure communications [6][7][8], etc.…”

Section: Introductionmentioning

confidence: 99%