A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

Lei, Junwei; Wang, Xinyu; Lei, Yinhua

doi:10.1016/j.cnsns.2008.12.010

Cited by 33 publications

(20 citation statements)

References 9 publications

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“…Chaos systems have complex dynamical behaviors that possess some special features such as being extremely sensitive to tiny variations of initial conditions [1][2][3][4], and having bounded trajectories with a positive leading Lyapunov exponent and so on. In recent years, chaos synchronization has attracted increasingly attentions due to their potential applications of secure communications.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of the Modified Chua’s Circuits with a Derivative Filter

Sun

Wang

Lei

2011

Advances in Computer Science, Environment, Ecoinformatics, and Education

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Abstract.A novel derivative filter is firstly proposed in this paper and it is used in the synchronization of Chua's Chaotic system with unknown parameters. It is described with transfer function so it makes use of the advantage of classical control theory. Also, it can absorb the merit of the modern control theory such as Lyapunov stability theorem. But the defect of this paper is that this paper is based on the assumption that three parameters in filters are small enough. So in our future work, a new analysis method will be researched which can relax this assumption.

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Section: Introductionmentioning

confidence: 99%

Synchronization of the Modified Chua’s Circuits with a Derivative Filter

Sun

Wang

Lei

2011

Advances in Computer Science, Environment, Ecoinformatics, and Education

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“…Double integral strategy is a new technology and it can be powerful if it is integrated with Lyapunov theorem properly. Chaos systems have complex dynamical behaviors that possess some special features such as being extremely sensitive to tiny variations of initial conditions [1][2][3][4], and having bounded trajectories with a positive leading Lyapunov exponent and so on. In recent years, chaos synchronization has attracted increasingly attentions due to their potential applications of secure communications.…”

Section: Introductionmentioning

confidence: 99%

Double Integral Adaptive Synchronization of the Lorenz Chaotic Systems with Unknown Parameters

Sun

Wang

Lei

2011

Advances in Computer Science, Environment, Ecoinformatics, and Education

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Abstract.A novel double integral action is firstly proposed in this paper and it is integrated with a novel integral Lyapunov function, which is necessary to analyze the system stability. The synchronization of chaotic system with unknown parameters are fulfilled by the constructing of Lyapunov function and the adopting of double integral action. Also, a filter is applied to make the controller is more flexible. But it is necessary to assume that the filter parameter is small enough when the stability of whole system is analyzed.

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“…The Nussbaum gain theory is used to cope with unknown control gain. 20,21 Then, the unknown items can be estimated accurately with the Nussbaum gain. Unfortunately, the calculation is very complicated and time consuming.…”

Section: Introductionmentioning

confidence: 99%

Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights

Luo

Wu²,

Gao

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.

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A Nussbaum gain adaptive synchronization of a new hyperchaotic system with input uncertainties and unknown parameters

Cited by 33 publications

References 9 publications

Synchronization of the Modified Chua’s Circuits with a Derivative Filter

Synchronization of the Modified Chua’s Circuits with a Derivative Filter

Double Integral Adaptive Synchronization of the Lorenz Chaotic Systems with Unknown Parameters

Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights

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