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

Kirubhakaran Krishnanathan, Sean R. Anderson, Stephen A. Billings and Visakan Kadirkamanathan

International Journal of Systems Science, 2016, vol. 47, issue 15, 3537-3544

Abstract: 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.

Date: 2016
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DOI: 10.1080/00207721.2015.1090643

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