Abstract (EN)

Given a mathematical model of a physical process, the parameter identification problem is defined as that of determining the parameters of the model that, for a known given input, yield a given measured output. Identifiability is often defined as the injectivity of the parameter → output mapping defined by the mathematical model used. Though already this definition is difficult to check in practical situations, it is not guaranteed, when it is satisfied, that parameters can be determined in a unique and stable way from the measurement. So we will review some recent definitions as OLS-Stability, OLS-identifiability and δ-Identifiability. Two different ways of obtaining OLSI will be given: either by studying the injectivity of the linearized parameter → output mapping (the “sensitivity matrix”), which will yield OLSI for finite dimensional parameters, but will usually be of little help for infinite dimensional parameters, or by using a regularization technique, which will be shown to yield OLSI for a large enough regularization parameter.