Quantification of Uncertainty in Estimation using an Embedding Principle

In this paper a new method to quantify uncertainty due to undermodelling is presented. The unmodelled dynamics are embedded in a general class of systems which is defined using realistic a priori information. This embedding principle can be formalized in several different ways; the one presented in this paper involves the setting of a stochastic framework, where the unmodelled dynamics are taken to be a particular realization of a Stochastic Embedding Process (S.E.P.) A priori knowledge is used to choose suitable statistics for this process. This approach allows one to quantify the effect of the modelling errors on the estimated transfer function in the frequency domain. The principal advantage of this approach is that it allows one to consider robust and adaptive control within the same conceptual framework.