R. Delgado Pulgar:

"Rank Constraints and Error Quanti cation in Restricted Complexity Problems";

Betreuer/in(nen), Begutachter/in(nen): G. Goodwin, M. Deistler; University of Newcastle, 2014.

This thesis addresses two issues that arise in restricted complexity estimation problems: The rst

is estimation subject to rank constraints. The second corresponds to uncertainty quanti cation

when the amount of data available is small relative to the number of variables to be estimated.

In many practical problems one wishes to choose a simple solution from a set of possible solutions.

The reasons for this can be many fold. For example, in design problems, one may know that a

simple solution is possible. However, one does not know how to obtain such a simple solution from

a large set of possible alternatives. In estimation problems, one may deliberately restrict the set of

possible solutions to avoid over- tting of noisy data. We term the class of problems having simple

solutions restricted complexity problems.

The rst part of the thesis address restricted problems where the restriction on complexity can be

related to constraining the rank of a particular matrix. This leads us to address rank-constrained

optimization problems.

The second part of the thesis focuses on quanti cation of estimation-error. It is well known that,

when the amount of data available for estimation is small, the variance error could be signi cantly

large. In these circumstances it is bene cial to, not only, have an estimated value for the parameters

but also to be able to quantify the associated error. However, most of the existing methods for error

quanti cation rely upon asymptotic results with large data. We focus on parametric uncertainty

quanti cation for nite data estimation, with an extension to the related problem of moving horizon

estimation.

The third part of the thesis, focuses on quanti cation of estimation errors when the complexity of

the model is deliberately chosen to be smaller than the complexity of the \true" model. This has

motivated a novel approach, commonly known in the literature by the generic title \model error

modelling", to uncertainty quanti cation. This has been a central theme in several areas including

statistics, time series analysis, econometrics and system identi cation. In the third part of the

thesis we address the problem of model error modelling for dynamic system identi cation.

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.