On the role of noise models for approximate closed loop identification

Schemes for system identification, based on closed-loop experiments, have attracted considerable interest lately. One reason for this is that such schemes naturally arise when the ultimate objective of the identification is to use the model for control design ('identification for control'). In this note we take a look at the problem of choosing a model structure which reflects the purpose of the identification, and in particular the role the noise model plays. It is shown that several of the schemes for closed-loop identification, suggested in the literature, are based on a particular choice of noise model. This noise model can be motivated from the desire to make the identification and control criteria identical.