Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

Li, Xianfeng; Leung, Chi-Sing; Liu, Xiaojun; Han, Xiuping; Chu, Yan-Dong

doi:10.1016/j.nonrwa.2009.06.011

Cited by 28 publications

(30 citation statements)

References 23 publications

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“…These include the adaptive control strategy [9], projective synchronization [10], sliding mode control [11], nonlinear control techniques [12], and active control method [13], which are well-known synchronization control techniques among others. Among these techniques, the active control (AC) and adaptive synchronization control (ASC) strategies have attracted a great interest in the literature concerned because of their easy implementation to practical systems [14][15][16][17][18][19][20][21][22]. The AC method for the chaos synchronization was first proposed in [17] based on the active control theory [23] and further studied by many researchers [24][25][26] among others.…”

Section: Introductionmentioning

confidence: 99%

“…From the literature survey, it has also been established that while using the ASC approaches [18][19][20][21][22] (among others), the feedback control functions for the CS of two coupled chaotic (or hyperchaotic) systems have been developed so that the amplitude of the oscillation of the error signals and the synchronization transient time are large. However, the variations in amplitude of the oscillation of the error signals cannot be evaded during the transmission of a chaotic signal, which actually determines the amount of energy to transmit the chaotic signals from transmitter to receiver.…”

Section: Introductionmentioning

confidence: 99%

“…Likewise, the time response is an important feature in real-time applications such as communication networks as they depend on the time synchronization between different nodes [29]. Furthermore, in [18][19][20][21][22], the unknown parameters are assumed to be constant and the chaotic systems are considered free of the unknown model uncertainties and external disturbances. These perturbations are not integrated into the system dynamics altogether due to the analytical and computational stability complications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Ahmad

Saaban

Ibrahim

2017

J. Uncertain. Anal. Appl.

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In this paper, a synchronization problem of a three-dimensional (3-D) Coullete chaotic system using the active-and adaptive-based synchronization control techniques is addressed. Based on the Routh-Hurwitz criterion and using the active control algorithm, a single control function is considered and a computational study is performed to identify the correct balance between the converging rates of the synchronization error signals to the origin and magnitude of the linear controlling parameters (LCPs) for the globally exponential synchronization (GES) between two identical 3-D Coullete chaotic systems. In order to achieve the complete synchronization (CS) objective with unknown model uncertainties, external disturbances, and unknown time-varying parameters, a novel nonlinear adaptive synchronous controller is proposed and suitable adaptive laws of time-varying parameters are designed that accomplish the asymptotic synchronization between two identical uncertain 3-D Coullete chaotic systems. The two synchronizing controlling approaches are applied to investigate the CS phenomenon, and the results are compared. Open research problems are also discussed. All simulations results are carried out to validate the effectiveness of the proposed synchronization control approaches by using Mathematica 10.0.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Ahmad

Saaban

Ibrahim

2017

J. Uncertain. Anal. Appl.

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“…As a result, a wide range of synchronization and AS control techniques and methods have been proposed. These include sliding mode control [6], active control [7], non-linear control [8], periodically intermittent control [9], adaptive control [10], H-∞ synchronization [11], projective synchronization [12], and generalized synchronization [13], etc. Anti-synchronization (AS) is a special form of generalized synchronization.…”

Section: Introductionmentioning

confidence: 99%

Robust Finite-Time Anti-Synchronization of Chaotic Systems with Different Dimensions

et al. 2015

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Abstract:In this paper, we demonstrate that anti-synchronization (AS) phenomena of chaotic systems with different dimensions can coexist in the finite-time with under the effect of both unknown model uncertainty and external disturbance. Based on the finite-time stability theory and using the master-slave system AS scheme, a generalized approach for the finite-time AS is proposed that guarantee the global stability of the closed-loop for reduced order and increased order AS in the finite time. Numerical simulation results further verify the robustness and effectiveness of the proposed finite-time reduced order and increased order AS schemes.

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“…Therefore, synchronization of two different chaotic and hyper-chaotic systems with uncertain parameters is more essential and realistic in actual applications. [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] used adaptive control techniques to synchronize two identical or different chaotic or hyper-chaotic systems. However, their researches only concern some special chaotic and hyper-chaotic systems with uncertain parameters.…”

Section: Introductionmentioning

confidence: 99%

Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control

Leung

Han

et al. 2010

Nonlinear Dyn

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This paper addresses a unified mathematical expression describing a class of chaotic systems, for which the problem of synchronization and antisynchronization between different chaotic systems with fully uncertain parameters and different structure are studied. Based on the Lyapunov stability theory, a novel, simple, and systemic adaptive synchronization controller is designated, the analytic expression of the controller and the adaptive laws of parameters are developed. Moreover, the proposed scheme can be extended to anti-synchronize a class of chaotic systems. Two chaotic systems with different structure and fully uncertain parameters are employed as the examples to show the effectiveness of the proposed adaptive synchronization and anti-synchronization schemes. Additionally, the robustness and noise immunity of

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Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters

Cited by 28 publications

References 23 publications

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

Robust Finite-Time Anti-Synchronization of Chaotic Systems with Different Dimensions

Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control

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