System Identification in Highly Non-Informative Environment

Samenvatting

System identification has gone a long way in the past century but there are still problems to be solved and new directions waiting to be discovered. The mainstream identification literature contains results that rely on practically infinite amount of data (either measurement data or prior knowledge), which is acceptable compromise for many applications, but not for all. The focus in this thesis is put on obtaining statistically reliable uncertainty estimates when the identification task is carried out in a non-informative environment, meaning that the number of observations and that of the estimated parameters is barely enough to make the estimation problem meaningful. As this problem is tackled, a series of questions emerge that serve as the subject of the thesis. First, a recent method (Sign-Perturbed Sums, SPS) for constructing exact confidence regions is described from a new point of view by defining a generic family of such methods (Data Perturbation methods, DP methods). Exact confidence level hypothesis tests can be constructed in the framework of DP methods where some of the elements of a DP method are determined by the assumed characteristics of the noise that contaminates the measurements. The other elements need to be defined to suit the model structure that is estimated. It is shown that the SPS method is a DP method belonging to symmetrically distributed noise sources. Other DP methods are also given and the structure of the corresponding confidence sets is examined. DP methods for parameter estimates of linear dynamical systems rely on the solution of polynomial optimization problems. The second part of the thesis deals with how the optimum of such problems can be obtained in light of recent developments in the optimization community. As computing exact confidence regions turns out to be computationally taxing, it needs to be quantified when the asymptotic results can be trusted. The last part of the thesis describes a method that estimates the uncertainty error introduced by asymptotic results. Based on these estimates it can be decided whether the asymptotic confidence regions are to be trusted or some sort of compensation is needed.

Datum prijs	14 jan 2016
Originele taal	English
Prijsuitreikende instantie	Budapest University of Technology and Economics
Begeleider	Istvan Vajk (Promotor) & Joannes Schoukens (Promotor)