Comparing Different Approaches to Model Error Modeling in Robust Identification

Identification for robust control must deliver not only a nominal model, but also a reliable estimate of the uncertainty associated with the model. This paper addresses recent approaches to robust identification, that aim at dealing with contributions from the two main uncertainty sources: unmodeled dynamics and noise affecting the data. In particular, non-stationary Stochastic Embedding, Model Error Modeling based on prediction error methods and Set Membership Identification are considered. Moreover, we show how Set Membership Identification can be embedded into a Model Error Modeling framework. Model validation issues are easily addressed in the proposed framework. A discussion of asymptotic properties of all methods is presented. For all three methods, uncertainty is evaluated in terms of the frequency response, so that it can be handled by H8 control techniques. An example, where a nontrivial undermodeling is ensured by the presence of a nonlinearity in the system generating the data, is presented to compare these methods.