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On the control of unknown continuous time chaotic systems by applying Takens embedding theory

Author

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  • Kaveh, H.
  • Salarieh, H.
  • Hajiloo, R.

Abstract

In this paper, a new approach to control continuous time chaotic systems with an unknown governing equation and limitation on the measurement of states, has been investigated. In many chaotic systems, disability to measure all of the states is a usual limitation, like in some economical, biological and many other engineering systems. Takens showed that a chaotic attractor has an astonishing feature in which it can embed to a mathematically similar attractor by using time series of one of the states. The new embedded attractor saves much information from the original attractor. This phenomenon has been deployed to present a new way to control continuous time chaotic systems, when only one of the states of the system is measurable and the system model is not also available.

Suggested Citation

  • Kaveh, H. & Salarieh, H. & Hajiloo, R., 2018. "On the control of unknown continuous time chaotic systems by applying Takens embedding theory," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 53-57.
    • Handle: RePEc:eee:chsofr:v:109:y:2018:i:c:p:53-57
    DOI: 10.1016/j.chaos.2018.02.012
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    References listed on IDEAS

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    1. Salarieh, Hassan & Alasty, Aria, 2009. "Chaos control in an economic model via minimum entropy strategy," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 839-847.
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    Cited by:

    1. Jokar, Meysam & Salarieh, Hassan & Alasty, Aria, 2019. "On the existence of proper stochastic Markov models for statistical reconstruction and prediction of chaotic time series," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 373-382.
    2. Kaveh, Hojjat & Salarieh, Hassan, 2020. "A new approach to extreme event prediction and mitigation via Markov-model-based chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Fan, Zhenyi & Zhang, Chenkai & Wang, Yiming & Du, Baoxiang, 2023. "Construction, dynamic analysis and DSP implementation of a novel 3D discrete memristive hyperchaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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