A Criterion Based Approach to Parametrization and Identification of Multivariable Systems

Abstract

The problem of system identification is considered in terms of (approximate) modelling of a given sequence of measurement data. Given a data sequence of a multivariable process, there arc two aspects that play a central role in determining the properties of the identified models: the set of models that is taken into account, and the identification criterion that selects the identified models from this set. When parametrizing a set of models ℳ very often use is made of a notion of model equivalence in order to arrive at a uniquely identifiable model set ℳ* ⊂ ℳ It is undesirable that the dynamical properties of the identified model are dependent on the specific choice of ℳ*, i.e. the specific parametrization chosen; consequently it is shown that the applied model equivalence, which conventionally refers to input–output equivalence, has to be in accordance with the identification criterion. Therefore a criterion based model equivalence is introduced which for equation error identification methods leads to a non conventional set of canonical forms.