Identification of smooth nonlinear dynamical systems with non-smooth steady-state features

This work discusses the identification of single-block smooth nonlinear discrete-time polynomial models with non-smooth steady-state features. Based on bifurcation theory, conditions are developed and used to determine some general aspects of the model structure and also to determine some constraints on the parameters required to guarantee the aforementioned features. The procedure uses only smooth functions of the regressors, a single possibly smooth input and some prior knowledge about the steady-state behavior. The non-smooth static function is here obtained by interchanging the stability of two sets of equilibria at the break-point, which corresponds to guaranteeing a transcritical bifurcation. This work discusses how to determine the domain over which the results are valid. The procedure is illustrated with simulated and experimental data.