Impulsive control of Lorenz system

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

doi:10.1016/s0167-2789(97)00116-4

Cited by 181 publications

(95 citation statements)

References 8 publications

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“…During the last several decades, impulsive control theory has attracted considerable attention because impulsive control method can be employed in many fields, such as the stabilization and synchronization of chaotic systems [11][12][13][14] and complex dynamical networks [15][16][17][18][19]. For more results on impulsive control and its applications, the reader is referred to [11,20,21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

et al. 2017

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The purpose of this note is to study impulsive control and synchronization of memristor based chaotic circuits shown by Muthuswamy. We first establish a less conservative sufficient condition for the stability of memristor based chaotic circuits. After that, we discuss the effect of errors on stability. Meanwhile, we also discuss impulsive synchronization of two memristor based chaotic systems. Our results are more general and more applicable than the ones shown by Yang, Li, and Huang. Finally, several numerical examples are given to show the effectiveness of our methods.

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Section: Introductionmentioning

confidence: 99%

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

et al. 2017

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“…This leads to unavoidable and higher interference to the devices. The coexistence issue within the 2.4 GHz ISM band has been studied, and the result shows that IEEE 802.15.4 devices, which are part of WSN, seem to have a severe impact from other systems, especially from the IEEE 802.11 devices operating on an overlapping frequency band in the same area [1,2]. This is because IEEE 802.15.4 standard is designed for Low-Rate Wireless Personal Area Networks (LR-WPANs) with low transmission power devices.…”

Section: Introductionmentioning

confidence: 99%

Cognitive Wireless Sensor Networks: Intelligent Channel Assignment

Chantaraskul

Tanwongvarl

2017

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Abstract. One of the major problems in Wireless Sensor Networks (WSNs) is the traffic congestion caused by increasing number of devices sharing the limited spectrum of the ISM (Industrial, Scientific, and Medical radio) band. As a result, a new concept of Cognitive Wireless Sensor Networks (CWSNs) has been proposed in order to achieve reliable and efficient communication via spectrum awareness and smart adaption. Based on such concept, this paper proposes the intelligent channel assignment technique for channel management in CWSNs. The proposed method is based on the learning and prediction technique so called Policy Gradient together with our proposed virtual channel environment classification. Simulation model is used for the system performance evaluation. The simulation results show that our proposed intelligent channel assignment provides substantially higher performance in terms of system throughput and average packet end-to-end delay than the traditional IEEE 802.15.4 based system. It also outperforms the systems integrated with Episodic Reinforcement and GPOMDP learning technique.

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“…The theory of impulsive ordinary differential equations and its applications to the fields of science and engineering have been very active research topics [28][29][30][43][44][45], since the theory provides a natural framework for mathematical modeling of many physical phenomena. Furthermore, impulsive control, which is based on the theory of impulsive differential equations, has gained renewed interests recently for its promising applications towards controlling systems exhibiting chaotic behaviour.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, it was realized that, such a control method allows the stabilization of a chaotic system using only small control impulses, even though the chaotic behaviour may follow unpredictable patterns (in general, chaotic signals are broadband, noise like and difficult to predict). Examples include the impulsive control of autonomous systems of ODEÕs such as Lorenz system and ChuaÕs oscillator [29,43,45] and non-autonomous chaotic systems of ODEÕs, such as the DuffingÕs oscillator [42], where the stabilization of the chaotic system is achieved in a small region of the phase space using the notion of practical stability (instead of controlling the non-autonomous chaotic system to an equilibrium position).…”

Section: Introductionmentioning

confidence: 99%

Impulsive control and synchronization of spatiotemporal chaos

Khadra

Liu

Shen

2005

Chaos, Solitons & Fractals

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The impulsive control of spatiotemporal chaos of a particular type of non-linear partial differential equations has been investigated. A criterion for the solutions of these partial differential equations to be equi-attractive in the large is determined and an estimate for the basin of attraction is given in terms of the impulse durations and the magnitude of the impulses. Extending these results to impulsively synchronize spatiotemporal chaos of the same type of partial differential equations is explored. A proof for the existence of a certain kind of impulses for synchronization such that the error dynamics is equi-attractive in the large, is established. A comparison of the developed theoretical model with other existent numerical models available in the literature has been studied. Several simulation results are given to confirm the theoretical results. Moreover, an investigation of the Lyapunov exponents of the error dynamics between impulsively synchronized spatiotemporal chaotic systems, is done to further confirm the theoretical results.

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Impulsive control of Lorenz system

Cited by 181 publications

References 8 publications

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

Stabilization and Synchronization of Memristive Chaotic Circuits by Impulsive Control

Cognitive Wireless Sensor Networks: Intelligent Channel Assignment

Impulsive control and synchronization of spatiotemporal chaos

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