Adaptive synchronization of Lü system with uncertain parameters

Elabbasy, Elmetwally M.; Agiza, H.N.; El-Dessoky, M. M.

doi:10.1016/j.chaos.2003.12.028

Cited by 73 publications

(29 citation statements)

References 29 publications

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“…A chaotic system is a nonlinear deterministic system that displays complex and unpredictable behavior, which has more and more applications such as laser array, biological systems, chemical reactions, power converters, information processing, secure communication, information science, biotic science and so on [1,6,7,10,16,35,36]. Recently, control and synchronization of chaotic systems have been considerably studied in several fields (see, for example, [11,12,14,19,21,28,29,34] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Parameter identification of chaotic systems using improved differential evolution algorithm

Chou

Guo

2009

Nonlinear Dyn

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In this paper, an improved differential evolution algorithm, named the Taguchi-sliding-based differential evolution algorithm (TSBDEA), is proposed to solve the problem of parameter identification for Chen, Lü and Rossler chaotic systems. The TSBDEA, a powerful global numerical optimization method, combines the differential evolution algorithm (DEA) with the Taguchi-sliding-level method (TSLM). The TSLM is used as the crossover operation of the DEA. Then, the systematic reasoning ability of the TSLM is provided to select the better offspring to achieve the crossover, and consequently enhance the DEA. Therefore, the TSBDEA can be more robust, statistically sound, and quickly convergent. Three illustrative examples of parameter identification for Chen, Lü and Rossler chaotic systems are given to demonstrate the applicability of the proposed TSBDEA, and the computational experimental results show that the proposed TSBDEA not only can find optimal or close-to-optimal solutions but also can obtain both better and more robust results than the DEA.

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Section: Introductionmentioning

confidence: 99%

Parameter identification of chaotic systems using improved differential evolution algorithm

Chou

Guo

2009

Nonlinear Dyn

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“…T Therefore the synchronization of two Newton-Leipnik systems are achieved under the controller (11) and a parameter estimation and update law equation (12).…”

Section: Adaptive Synchronization Of Newton-leipnik System With All Pmentioning

confidence: 99%

“…studied synchronization of bidirectionally coupled chaotic Chen's system with delay in 2007 [9] and they also observed synchronization of generalised linearly bidirectionally coupled unified chaotic system in 2009 [10]. Synchronization via adaptive control has been successfully tested in variety of non-linear dynamical systems including Unified chaotic system, Lu system and Chen system [11,12,13]. In 1994 J.K.John and R.E.Amritkar have studied synchronization of unstable orbits using adaptive control [14].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive synchronization of two coupled Newton-Leipnik systems with uncertain parameter

Khan¹

2012

International Journal of Basic and Applied Sciences

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In this letter, an adaptive synchronization and parameters identification scheme is proposed for two coupled chaotic Newton-Leipnik systems. Based on Lyapunov stability theory an adaptive controller is designed to make the states of two identical chaotic Newton-Leipnik system with unknown system parameters asymptotically synchronized. Especially when some unknown parameters are positive, we can make the controller more simple, beside the controller is independent of those positive uncertain parameters. Numerical simulation results are presented to visualize the effectiveness and feasibility of the developed approaches.

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“…In the real application, most models of controlled system are uncertain or not accurate which makes the controller design to be a complex problem [1][2][3][4][5][6][7][8][9][10][11]. Some model are certain in some conditions, for example the parameters and the model of the controlled system will change unpredictably when conditions change.…”

Section: Introductionmentioning

confidence: 99%

Synchronous Control of Second Order Linear System Based on Sliding Mode Method

Li¹,

Ma²,

Wang³

et al. 2016

IJCA

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In order to solve the uncertain problem that parameters of system model are not accurate, a synchronous control method which is based on sliding mode method is proposed in this paper. A synchronous system which has the similar structures with the controlled system is constructed, then a control law is design to make the synchronous system trace the controlled system. So the controlled system can be controlled by controlling the synchronous system. Finally, numerical simulation was done the testify the rightness of the proposed method.

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Adaptive synchronization of Lü system with uncertain parameters

Cited by 73 publications

References 29 publications

Parameter identification of chaotic systems using improved differential evolution algorithm

Parameter identification of chaotic systems using improved differential evolution algorithm

Adaptive synchronization of two coupled Newton-Leipnik systems with uncertain parameter

Synchronous Control of Second Order Linear System Based on Sliding Mode Method

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