On evolutionary system identification with applications to nonlinear benchmarks

This paper presents a record of the participation of the authors in a workshop on nonlinear system identification held in 2016. It provides a summary of a keynote lecture by one of the authors and also gives an account of how the authors developed identification strategies and methods for a number of benchmark nonlinear systems presented as challenges, before and during the workshop. It is argued here that more general frameworks are now emerging for nonlinear system identification, which are capable of addressing substantial ranges of problems. One of these frameworks is based on evolutionary optimisation (EO); it is a framework developed by the authors in previous papers and extended here. As one might expect from the 'no-free-lunch' theorem for optimisation, the methodology is not particularly sensitive to the particular (EO) algorithm used, and a number of different variants are presented in this paper, some used for the first time in system identification problems, which show equal capability. In fact, the EO approach advocated in this paper succeeded in finding the best solutions to two of the three benchmark problems which motivated the workshop. The paper provides considerable discussion on the approaches used and makes a number of suggestions regarding best practice; one of the major new opportunities identified here concerns the application of grey-box models which combine the insight of any prior physical-law based models (white box) with the power of machine learners with universal approximation properties (black box).