Assessing the quality of identified models trough the asymptotic theory – When is the result reliable?

In this paper, the problem of estimating uncertainty regions for identified models is considered. A typical approach in this context is to resort to the asymptotic theory of Prediction Error Methods for system identification, by means of which ellipsoidal uncertainty regions can be constructedfor the uncertain parameters. We show that the uncertainty regions workedout through the asymptotic theory can be unreliable in certain situations, precisely characterizedin the paper. Then, we critically analyze the theoretical conditions for the validity of the asymptotic theory, and prove that the asymptotic theory also applies under new assumptions which are less restrictive than the usually required ones. Thanks to this result, we single out the classes of models among standard ones (ARX, ARMAX, Box–Jenkins, etc.) where the asymptotic theory can be safely used in practical applications to assess the quality of the identified model. These results are of interest in many applications, including iterative controller design schemes.