Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification

Feng, Jianwen; Chen, Shihua; Wang, Changping

doi:10.1016/j.chaos.2005.02.027

Cited by 40 publications

(13 citation statements)

References 17 publications

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“…Therefore, in this paper, adaptive control method is adopted to study the synchronization problem of GLHS under the assumption that the parameters of the drive system are unknown and different from those of the response system. Furthermore, by introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper has brand new form compared with the former relative works [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 98%

“…Therefore, the synchronization problem of chaotic systems with unknown parameters is very important. This kind of synchronization problem has been studied for many hyperchaotic systems, including Rössler hyperchaotic system [7,8], hyperchaotic Chen system [9], hyperchaotic Lü system [10], Gao hyperchaotic system [11], and 4D Qi system [12].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive synchronization of GLHS with unknown parameters

Wang

Guo

Xiao

et al. 2008

Circuit Theory & Apps

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SUMMARYIn this paper, an adaptive controller for the synchronization of two generalized Lorenz hyperchaos systems (GLHSs) is designed by using the Lyapunov method. In the synchronization schema, the parameters of the drive system are unknown and different from those of the response system. By introducing update laws for both the control coefficients and the parameters of the response system, the adaptive controller proposed in this paper is brand new compared with the former relative works. The proposed adaptive controller is feasible for any possible parameters of GLHS. Numerical simulation is carried out to verify and illustrate the analytical result.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Adaptive synchronization of GLHS with unknown parameters

Wang

Guo

Xiao

et al. 2008

Circuit Theory & Apps

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“…Some of the methods applied in chaos control and synchronization have been extended to hyperchaos control and synchronization. These include linear and nonlinear feedback control/synchronization [13,14,18,19,24,25,27], adaptive control/synchronization [16,[27][28][29][30][31][32], backstepping techniques [12,17], lag control/synchronization [20,21], active control [22], impulsive synchronization [23], sliding mode synchronization [26], and the Pecora-Carroll method [27]. Despite the numerous advantages inherent in the backstepping techniques as discussed earlier, its application in hyperchaos control and synchronization has not been adequately investigated.…”

mentioning

confidence: 98%

“…Hence, control and synchronization of hyperchaotic systems are believed to have wider applications than those of chaotic systems. Motivated by this, a lot of effort has been devoted by researchers in achieving the goals of hyperchaos control [13][14][15][16][17][18][19] and synchronization [12,[20][21][22][23][24][25][26][27][28][29][30][31][32]. Hyperchaos control and synchronization, however, poses more challenges as a result of the fact that they are of higher dimensions and exhibit more complex dynamics than chaotic systems.…”

mentioning

confidence: 99%

Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques

Njah

2009

Nonlinear Dyn

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In this paper, recursive and active backstepping nonlinear techniques are employed to design control functions for the respective, control, and synchronization of the new hyperchaotic Liu system. The designed recursive backstepping nonlinear controllers are capable of stabilizing the hyperchaotic Liu system at any position as well as controlling it to track any trajectory that is a smooth function of time. The designed active backstepping nonlinear controllers are effective in globally synchronizing two identical hyperchaotic Liu systems evolving from different initial conditions. The results are all validated by numerical simulations.

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“…A very promising chaos control strategy, that is lately being explored is the 'adaptive' approach [16][17][18][19]. Adaptive control [20,21] and synchronization [14,22,23] involves design of controllers, based on principle of engineering adaptive controllers.…”

Section: Introductionmentioning

confidence: 99%

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

Islam¹,

Islam²,

Николов³

2015

Journal of Theoretical and Applied Mechanics

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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 unknown 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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Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification

Cited by 40 publications

References 17 publications

Adaptive synchronization of GLHS with unknown parameters

Adaptive synchronization of GLHS with unknown parameters

Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques

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

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