Tuning nonlinear state-space models using unconstrained multiple shooting

A persisting challenge in nonlinear dynamical modelling is parameter inference from data. Provided that an appropriate model structure was selected, the identification problem is profoundly affected by a choice of initialisation. A particular challenge that may arise is initialisation within a region of the parameter space where the model is not contractive. Exploring such regions is not feasible using the conventional optimisation tools for they require a bounded evaluation of the cost. This work proposes an unconstrained multiple shooting technique, able to mitigate stability issues during the optimisation of nonlinear state-space models. The technique is illustrated on simulation results of a Van der Pol oscillator and benchmark results on a Bouc-Wen hysteretic system.