On the Interplay Between Model Uncertainty and Data Disturbances

Abstract

The Redheffer star product is used in the context of system identification. It is shown that for given input-output data and given a-priori bounds of the noise, an upper- bound on the model uncertainty can be derived. We show that for a fixed model the true model error can be expressed as a star product of a matrix G and an unknown matrix Qt- The matrix G is built up from information concerning the model, the model error structure, the measured data and the noise bounding functions. The matrix Qt represents the disturbance, which is assumed to belong to a set of norm bounded operators. If a-priori bounds of the disturbances are available, then an upper bound on the model uncertainty can be given. The identification problem consist in finding a model which minimizes this upper bound.