Computational system identification of continuous-time nonlinear systems using approximate Bayesian computation

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Krishnanathan, K. ; Anderson, S.R. ; Billings, S.A. ; Kadirkamanathan, V. (2015)
  • Publisher: Taylor & Francis

In this paper, we derive a system identification framework for continuous-time nonlinear systems, for the first time using a simulation-focused computational Bayesian approach. Simulation approaches to nonlinear system identification have been shown to outperform regression methods under certain conditions, such as non-persistently exciting inputs and fast-sampling. We use the approximate Bayesian computation (ABC) algorithm to perform simulation-based inference of model parameters. The framework has the following main advantages: (1) parameter distributions are intrinsically generated, giving the user a clear description of uncertainty, (2) the simulation approach avoids the difficult problem of estimating signal derivatives as is common with other continuous-time methods, and (3) as noted above, the simulation approach improves identification under conditions of non-persistently exciting inputs and fast-sampling. Term selection is performed by judging parameter significance using parameter distributions that are intrinsically generated as part of the ABC procedure. The results from a numerical example demonstrate that the method performs well in noisy scenarios, especially in comparison to competing techniques that rely on signal derivative estimation.
  • References (36)
    36 references, page 1 of 4

    Anderson, S. R., & Kadirkamanathan, V. (2007). Modelling and identification of non-linear deterministic systems in the delta-domain. Automatica, 43 (11), 1859-1868.

    Anderson, S. R., Lepora, N. F., Porrill, J., & Dean, P. (2010). Nonlinear dynamic modeling of isometric force production in primate eye muscle. IEEE Transactions on Biomedical Engineering , 57 (7), 1554-1567.

    Baldacchino, T., Anderson, S. R., & Kadirkamanathan, V. (2012). Structure detection and parameter estimation for NARX models in a unified EM framework. Automatica, 48 (5), 857-865.

    Baldacchino, T., Anderson, S. R., & Kadirkamanathan, V. (2013). Computational system identification for Bayesian NARMAX modelling. Automatica, 49 , 2641-2651.

    Beaumont, M. A. (2010). Approximate Bayesian computation in evolution and ecology. Annual Review of Ecology, Evolution, and Systematics, 41 , 379-406.

    Beaumont, M. A., Zhang, W., & Balding, D. J. . (2002). Approximate Bayesian computation in population genetics. Genetics, 162 , 2025-2035.

    Billings, S. A. (2013). Nonlinear system identification: Narmax, methods in the time, frequency, and spatiotemporal domains. Wiley.

    Cha, S.-H., & Srihari, S. N. (2002). On measuring the distance between histograms. Pattern Recognition, 35 (6), 1355-1370.

    Chen, S., Billings, S. A., & Luo, W. (1989). Orthogonal least squares methods and their application to non-linear system identification. International Journal of control , 50 (5), 1873-1896.

    Coca, D., & Billings, S. (1999). A direct approach to identification of nonlinear differential models from discrete data. Mechanical Systems and Signal Processing, 13 (5), 739-755.

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