Nonlinear recursive chaos control

Harb, Ahmad; Zaher, Ashraf A.; Zohdy, Mohammed

doi:10.1109/acc.2002.1023974

Cited by 19 publications

(7 citation statements)

References 5 publications

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“…We selected the feedback coefficient k=45, so that the inequality (10) holds. According to Theorem 2, we know that the controlled system (6) is asymptotically stabilized at S 0 =(0,0,0,0). The initial states of the system are x(0)=2, y(0)=3, z(0)=1.5, w(0)=0.…”

Section: A Speed Feedback Controllermentioning

confidence: 99%

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Stabilizing unstable equilibrium point of hyperchaotic Lorenz system

Liu

Cao

2008

2008 7th World Congress on Intelligent Control and Automation

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Some basic properties of the hyperchaotic Lorenz system were analyzed, and the state feedback control methods were introduced for stabilizing unstable equilibrium point of the hyperchaotic system. The feedback controllers utilized the speed and hyperbolic function, respectively. Based on Routh-Hurwitz theorem, the span of the feedback coefficients was derived. Numerical simulations are given for illustration and verification. These methods are robust against system parametric variations, and can strongly reject external constant disturbances.

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Section: A Speed Feedback Controllermentioning

confidence: 99%

“…Due to its great potential of application, many methods and techniques have been proposed to achieve chaos control. For instance, feedback control [2,3], Lyapunov function methods [4], adaptive control [5], and nonlinear recursive control [6], etc.…”

Section: Introductionmentioning

confidence: 99%

Stabilizing unstable equilibrium point of hyperchaotic Lorenz system

Liu

Cao

2008

2008 7th World Congress on Intelligent Control and Automation

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“…Oscillators using recursive back stepping Control [3]. In this paper, we will continue on the work that was presented earlier by showing a solution for the Van der Pol oscillator as well.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators

Alghassab¹,

Mahmoud²,

Zohdy³

2017

IJMNTA

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This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping. A first order actuator is added to both models to expand on the chaotic behavior of the oscillators. In order to control the system without comprising linearization, Lyapunov non-linear control was used. A control Lyapunov function was tailored to the system. This led to improved maneuverability of the controller and the performance of the overall system. The controller was found to be highly efficient in system tracking and had swift response time. Simulations were performed on both the uncontrolled and controlled cases. Both simulation results ultimately confirmed the effectiveness of the proposed controller.

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“…In practice, chaos in mechanical and structural systems is not desirable because it may lead to irregular operations and fatigue failure. 17,18 Moreover, chaos can restrict the operating range of many mechanical, structural and electronic systems. Usually, whenever an irregular, unpredictable motion occurs in an engineering or technological device, the need arises to take some action in order to turn it into a predictable one or to stop any oscillations altogether.…”

Section: Introductionmentioning

confidence: 99%

Controlling Chaos in a Chua's Circuit Using Notch Filters

Zaher

Abu-Rezq

2009

J CIRCUIT SYST COMP

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This paper explores the use of notch filters for the purpose of damping out chaotic oscillations. The design of the filter and the way it is interfaced to the system are investigated from a signal-processing point of view. A Chua's circuit, that has typical applications in synchronization and secure communications, is used to exemplify the suggested methodology where both theoretical and experimental results are provided. The power spectrum of the original system is analyzed to selectively damp-out portions of the power spectrum, thus truncating period-doubling, the original cause of chaos. Both single and double notch filters are explored to examine their effect on the performance of the modified system. Steady state analysis as well as issues regarding practical implementation are addressed and advantages and limitations of the proposed method are highlighted.

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Nonlinear recursive chaos control

Cited by 19 publications

References 5 publications

Stabilizing unstable equilibrium point of hyperchaotic Lorenz system

Stabilizing unstable equilibrium point of hyperchaotic Lorenz system

Nonlinear Control of Chaotic Forced Duffing and Van der Pol Oscillators

Controlling Chaos in a Chua's Circuit Using Notch Filters

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