Continuous-time nonlinear systems identification with output error method based on derivative-free optimisation

The purpose of this study is to tackle the nonlinear system identification benchmarks proposed by (Schoukens and Noël, 2016). Two of the three benchmarks are considered, namely the cascaded tanks setup and the Bouc-Wen hysteretic system. Our approach is an output error method based on continuous time models. Due to the nonlinearities, the derivatives of the output with respect to the parameters are not defined everywhere. We compare the performance of two derivative-free optimisation solvers: the Nelder-Mead simplex and the NOMAD algorithm. Both are available in the OPTI Toolbox. The results suggest that the method is appropriate for those systems. However, it is not possible to discriminate between both optimisation solvers.