Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point

Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou; Yin, Peifeng; Wang, Binghong

doi:10.1063/1.4922837

Title: Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point

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Abstract

The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.

Authors:

Shao, Chenxi; Xue, Yong; Fang, Fang; Bai, Fangzhou ^[1]; Yin, Peifeng ^[2]; Wang, Binghong ^[3]

Department of Computer Science and Technology, University of Science and Technology of China, Hefei 230027 (China)
Department of Computer Science and Engineering, Pennsylvania State University, State College, Pennsylvania 16801 (United States)
Department of Modern Physics, University of Science and Technology of China, Hefei 230026 (China)

Publication Date:: Wed Jul 15 00:00:00 EDT 2015

OSTI Identifier:: 22483215

Resource Type:: Journal Article

Journal Name:: Chaos (Woodbury, N. Y.)

Additional Journal Information:: Journal Volume: 25; Journal Issue: 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; CHAOS THEORY; CONTROL; FEEDBACK; ORBITS; OSCILLATORS; PERIODICITY; PHASE DIAGRAMS; SIGNALS

Citation Formats


                    Shao, Chenxi, Xue, Yong, Fang, Fang, Bai, Fangzhou, Yin, Peifeng, and Wang, Binghong. Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4922837.

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                    Shao, Chenxi, Xue, Yong, Fang, Fang, Bai, Fangzhou, Yin, Peifeng, & Wang, Binghong. Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point.  United States.  https://doi.org/10.1063/1.4922837

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                    Shao, Chenxi, Xue, Yong, Fang, Fang, Bai, Fangzhou, Yin, Peifeng, and Wang, Binghong. 2015.  
        "Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point".  United States.  https://doi.org/10.1063/1.4922837.

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@article{osti_22483215,

  title        = {Series-nonuniform rational B-spline signal feedback: From chaos to any embedded periodic orbit or target point},

  author       = {Shao, Chenxi and Xue, Yong and Fang, Fang and Bai, Fangzhou and Yin, Peifeng and Wang, Binghong},

  abstractNote = {The self-controlling feedback control method requires an external periodic oscillator with special design, which is technically challenging. This paper proposes a chaos control method based on time series non-uniform rational B-splines (SNURBS for short) signal feedback. It first builds the chaos phase diagram or chaotic attractor with the sampled chaotic time series and any target orbit can then be explicitly chosen according to the actual demand. Second, we use the discrete timing sequence selected from the specific target orbit to build the corresponding external SNURBS chaos periodic signal, whose difference from the system current output is used as the feedback control signal. Finally, by properly adjusting the feedback weight, we can quickly lead the system to an expected status. We demonstrate both the effectiveness and efficiency of our method by applying it to two classic chaotic systems, i.e., the Van der Pol oscillator and the Lorenz chaotic system. Further, our experimental results show that compared with delayed feedback control, our method takes less time to obtain the target point or periodic orbit (from the starting point) and that its parameters can be fine-tuned more easily.},

  doi          = {10.1063/1.4922837},

  url          = {https://www.osti.gov/biblio/22483215},
  journal      = {Chaos (Woodbury, N. Y.)},

  issn         = {1054-1500},

  number       = 7,

  volume       = 25,

  place        = {United States},

  year         = {Wed Jul 15 00:00:00 EDT 2015},

  month        = {Wed Jul 15 00:00:00 EDT 2015}

}

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