Parametric Identification of Nonlinear Systems: Guaranteed Confidence Regions

In this paper we consider the problem of constructing confidence regions for the parameters of nonlinear dynamical systems. The proposed method extends a previous algorithm presented by Campi and Weyer \cite{CampiWeyer03,CampiWeyer04}. The generalization relies on the use of higher orderd statistics. The confidence regions are valid for any finite number of data samples and they are nonconservative, in the sense that they contain the parameter value with an exact probability. The usefulness of the proposed approach is illustrated on some simple examples. The present paper is a draft version of a more detailed and complete work which is still underway.