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Cost function based on hidden Markov models for parameter estimation of chaotic systems

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Abstract

In this note, we deal with parameter estimation methods of chaotic systems. The parameter estimation of the chaotic systems has some significant issues due to their butterfly effects. It can be formulated as an optimization problem and needs a suitable cost function. In this paper, we propose a new cost function based on a hidden Markov model which is a statistical tool for modeling of time series data. It can model dynamical characteristics of the chaotic systems. Moreover, the use of dynamical features of their strange attractors is investigated to achieve a better cost function in the procedure of parameter estimation. Our experimental results indicate the success of the proposed cost function in the one-dimensional parameter estimation of a new four-dimensional chaotic system and Lorenz system as a well-known three-dimensional chaotic system.

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Acknowledgements

This work was supported by the research grant from Shahid Beheshti University G.C. (Grant Number SAAD-600-1076). Sajad Jafari was supported by Iran National Science Foundation (No. 96000815).

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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. Center for Nonlinear Dynamics, College of Engineering, Defence University, Bishoftu, Ethiopia

    Karthikeyan Rajagopal

Authors
  1. Yasser Shekofteh
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  2. Sajad Jafari
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  3. Karthikeyan Rajagopal
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Contributions

Yasser Shekofteh designed the study and contributed to the experiment and algorithm design. Yasser Shekofteh and Sajad Jafari wrote the paper. Sajad Jafari and Karthikeyan Rajagopal performed the chaotic analysis of the paper.

Corresponding author

Correspondence to Yasser Shekofteh.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

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Shekofteh, Y., Jafari, S. & Rajagopal, K. Cost function based on hidden Markov models for parameter estimation of chaotic systems. Soft Comput 23, 4765–4776 (2019). https://doi.org/10.1007/s00500-018-3129-6

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