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K. Pattis:
"Optimal Control Problems - Chaos Expansion Approach";
Betreuer/in(nen): T. Levajković, M. Oberguggenberger; Fakultät für Mathematik, Informatik und Physik, Universität Innsbruck, 2019; Abschlussprüfung: 11.10.2019.

In this work, we study optimal control problems in the framework of white noise analysis. The aim of this thesis is to give a potential reader a short introduction into the area of optimal control theory and present some of its applications. Particularly, assuming that an optimal control exists, the main focus is on the study of necessary conditions that an optimal pair for a given optimal control problem has to satisfy. Therefore, different stochastic optimal control problems will be considered and depending on the particular problem, necessary conditions will be derived. Special emphasis will be on the study of stochastic linear quadratic optimal control problems. Necessary conditions for these problems will be formulated, which are generalizations of the results from the deterministic optimal control theory. The most important part of the thesis is the development of a unified approach which combines the chaos expansion method from white noise analysis with the deterministic optimal control results. These results represent the main contributions of the thesis.