Estimation of transfer functions: asymptotic theory and a bound of model uncertainty

Abstract

The problem of transfer function estimation is considered. We will discuss the problem in two (related) aspects: firstly, how to obtain a good black-box transfer function model; secondly, how to derive a suitable description of the model uncertainty (modelling errors). We will emphasize the second point. We shall discuss the asymptotic theory on the properties of transfer function estimates, developed recently by Ljung and Yuan. This new theory shows that the transfer function estimate is consistent, the error of the estimate is asymptotically normal, with a very simple expression for its variance. Their results will be extended here to cases where spectral analysis is used. Based on this theory, we will propose the method for obtaining a low-order nominal model of linear processes, and define and estimate an upper bound of the model uncertainty. An upper bound of the model uncertainty is a suitable description of the modelling errors for the robust controller design.