Controlling hyperchaotic Rabinovich system with single state controllers: Comparison of linear feedback, sliding mode, and passive control methods

Kocamaz, Uğur Erkin; Uyaroğlu, Yılmaz; Kizmaz, Hakan

doi:10.1016/j.ijleo.2016.11.006

Cited by 16 publications

(18 citation statements)

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“…In [32], some synchronization criteria were derived for 3D Rabinovich systems by using linear feedback control and Routh-Hurwitz criteria. But those results were local, rather than global.…”

Section: Complexitymentioning

confidence: 99%

“…In [13], some synchronization criteria were derived for 4D Rabinovich systems by the control which eliminated all the nonlinear terms of the error system. In [4,32], some synchronization criteria were obtained for 3D Rabinovich systems by using the sliding mode controls which also eliminated the nonlinear terms of the error system. Although the linear error systems can be easily obtained after the nonlinear terms of error systems were eliminated and synchronization criteria for linear error systems can also be easily derived, the nonlinear features in the original 4D hyperchaotic systems were discarded.…”

Section: Complexitymentioning

confidence: 99%

“…Master-slave synchronization of Rabinovich systems has been observed and attracted many researches' interests. In [32], some local synchronization criteria were derived for 3D Rabinovich systems by using linear feedback control and Routh-Hurwitz criteria. In [4,13,32], some synchronization criteria were derived for 3D or 4D Rabinovich systems by the control which eliminated all the nonlinear terms of the error system.…”

Section: Introductionmentioning

confidence: 99%

“…In [32], some local synchronization criteria were derived for 3D Rabinovich systems by using linear feedback control and Routh-Hurwitz criteria. In [4,13,32], some synchronization criteria were derived for 3D or 4D Rabinovich systems by the control which eliminated all the nonlinear terms of the error system. However, the Rabinovich systems are nonlinear systems in which the nonlinear terms play an important role in the dynamical evolution of trajectories.…”

Section: Introductionmentioning

confidence: 99%

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Master-Slave Synchronization of 4D Hyperchaotic Rabinovich Systems

Ding

Volos

et al. 2018

Complexity

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This paper is concerned with master-slave synchronization of 4D hyperchaotic Rabinovich systems. Compared with some existing papers, this paper has two contributions. The first contribution is that the nonlinear terms of error systems remained which inherit nonlinear features from master and slave 4D hyperchaotic Rabinovich systems, rather than discarding nonlinear features of original hyperchaotic Rabinovich systems and eliminating those nonlinear terms to derive linear error systems as the control methods in some existing papers. The second contribution is that the synchronization criteria of this paper are global rather than local synchronization results in some existing papers. In addition, those synchronization criteria and control methods for 4D hyperchaotic Rabinovich systems are extended to investigate the synchronization of 3D chaotic Rabinovich systems. The effectiveness of synchronization criteria is illustrated by three simulation examples.

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Section: Complexitymentioning

confidence: 99%

Section: Complexitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Master-Slave Synchronization of 4D Hyperchaotic Rabinovich Systems

Ding

Volos

et al. 2018

Complexity

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“…Since the pioneer study of Ott et al in 1990 [29], several effective methods for the control of chaotic systems have been proposed. The chaos control approaches include linear feedback control [13,15,16,18,22,24,41,44,47], nonlinear feedback control [7], time-delayed feedback control [34], adaptive control [2,40], sliding mode control [22,12], passive control [8,22,28,33,45], backstepping design [12,32], and intelligent control [20] methods. Among them, the linear feedback control has been widely used due to its simplicity of implementation.…”

Section: Introductionmentioning

confidence: 99%

Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

Kocamaz

Göksu

Uyaroğlu

et al. 2018

ITC

Self Cite

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In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed.

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