Implementation issues for a nonlinear version of the Hansen scheme

We propose a method for the identification of a nonlinear plant under possibly nonlinear feedback. This procedure is a nonlinear extension of a method known as the Hansen scheme in the literature. It is shown that using nonlinear left fractional descriptions one can convert a general nonlinear closed-loop identification problem to one of open-loop identification by parametrizing the model using a Youla-Kucera parameter. The open-loop problem can be implemented by parametrizing the nonlinear Youla parameter in terms of a model of the plant. We provide gradient expressions for implementation in a steepest descent algorithm