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Parameter Identification of Chaotic Systems Using a Modified Cost Function Including Static and Dynamic Information of Attractors in the State Space

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Abstract

Parameter identification (PI) is very important in system analysis and controller design and has wide applications in industry. PI is an essential step in designing mathematical models of the dynamical systems based on the measured data. Identification of chaotic systems is very challenging due to the butterfly effect. Recently, a state-space-based cost function based on Gaussian mixture model (GMM) has been proposed for the PI of the chaotic systems. In there, a GMM as a statistical model of the measured data modeled static features of the chaotic attractors in the state space. In this paper, we propose a new method which incorporates static and dynamic features in the GMM modeling in order to achieve a better cost function for the PI problem. The proposed method can extract suitable information from the trajectory of the chaotic attractor. We conduct some experiments for one-dimensional PI. Using measured data from 4D and 3D chaotic systems, empirical results indicate success of the proposed method.

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Acknowledgements

The work described in this paper was supported by the research Grant from Shahid Beheshti University G.C. (SAAD-600-1076).

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Authors and Affiliations

  1. Faculty of Computer Science and Engineering, Shahid Beheshti University, Velenjak, Tehran, 19839-69411, Iran

    Yasser Shekofteh

  2. Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran

    Sajad Jafari

  3. Department of Electronics Engineering, Durban University of Technology, Durban, South Africa

    Karthikeyan Rajagopal

  4. Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Viet-Thanh Pham

Authors
  1. Yasser Shekofteh
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  2. Sajad Jafari
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  3. Karthikeyan Rajagopal
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  4. Viet-Thanh Pham
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Correspondence to Yasser Shekofteh.

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Shekofteh, Y., Jafari, S., Rajagopal, K. et al. Parameter Identification of Chaotic Systems Using a Modified Cost Function Including Static and Dynamic Information of Attractors in the State Space. Circuits Syst Signal Process 38, 2039–2054 (2019). https://doi.org/10.1007/s00034-018-0967-5

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  • DOI: https://doi.org/10.1007/s00034-018-0967-5

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