Modified projective synchronization of fractional-order chaotic systems via active sliding mode control

Wang, Xingyuan; Zhang, Xiaopeng; Ma, Chao

doi:10.1007/s11071-011-0282-1

Cited by 130 publications

(76 citation statements)

References 13 publications

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“…All these forms of synchronization were first observed for the integer-order chaotic systems, then, were developed for fractional-order systems within the last decade. The publication of several papers on projective synchronization of fractional-order systems [25]- [32] and on the function projective synchronization of fractional-order systems [33]- [34] confirms this tendency. In ref.…”

Section: Introductionmentioning

confidence: 70%

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Kengne¹,

Tchitnga²,

Fomethe³

et al. 2017

Communications in Numerical Analysis

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This paper addresses the problem of generalized finite-time function projective synchronization (GFFPS) of fractionalorder chaotic systems. A modified fractional nonsingular terminal sliding mode surface and an appropriate robust fractional sliding mode control law are proposed, taking into account the effects of model uncertainties and of the external disturbances. An appropriate Lyapunov functional candidate is used to prove the finite-time existence of the sliding motion. Compared with the existing nonsingular sliding mode surface, our sliding mode surface permits to reduce the settling time of synchronization. Finally, some numerical simulations taking into consideration the Gaussian white noise produced by the electrical line are presented to demonstrate the effectiveness and applicability of the proposed technique.

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Section: Introductionmentioning

confidence: 70%

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Kengne¹,

Tchitnga²,

Fomethe³

et al. 2017

Communications in Numerical Analysis

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“…In this period, some projective synchronization types have been developed. Modified projective synchronization has been studied for a class of real nonlinear systems and a class of complex nonlinear systems [25][26][27]. On another research frontier, the combination synchronization has been investigated for secure communication, which can double the number of variables of the chaotic systems to strengthen the contents and security of the transmitted information.…”

Section: Introductionmentioning

confidence: 99%

Combination-Combination Projective Synchronization of Multiple Chaotic Systems Using Sliding Mode Control

Sun

Fang

2018

Advances in Mathematical Physics

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Based on projective synchronization and combination synchronization model, a type of combination-combination projective synchronization is realized via nonsingular sliding mode control technique for multiple different chaotic systems. Concretely, on the basic of the adaptive laws and stability theory, the corresponding sliding mode control surfaces and controllers are designed to achieve the combination-combination projective synchronization between the combination of two chaotic systems as drive system and the combination of multiple chaotic systems as response system with disturbances. Some criteria and corollaries are derived for combination-combination projective synchronization of the multiple different chaotic systems. Finally, the numerical simulation results are presented to demonstrate the effectiveness and correctness of the synchronization scheme.

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“…Moreover, different synchronization types have been presented in chaotic systems, such as phase synchronization [4], anti-synchronization [5], projective synchronization [6] and so on. Meanwhile, effective control methods have been proposed for various synchronization types.…”

Section: Introductionmentioning

confidence: 99%

Projective synchronization control of fractional-order chaotic system

Zhang¹

2018

Proceedings of the 2018 8th International Conference on Applied Science, Engineering and Technology (ICASET 2018)

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Abstract. This paper investigates projective synchronization of fractional order chaotic systems with different orders. In order to get the projective synchronization of fractional order chaotic systems with different orders, a scheme is proposed and effective controllers for synchronization are designed. Numerical simulations on examples are presented to show the effectiveness of the proposed control strategy.

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Modified projective synchronization of fractional-order chaotic systems via active sliding mode control

Cited by 130 publications

References 13 publications

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface

Combination-Combination Projective Synchronization of Multiple Chaotic Systems Using Sliding Mode Control

Projective synchronization control of fractional-order chaotic system

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