Stephen is a third-year Mathematics student at the University of Western Australia, interested in the fields of differential geometry and variational calculus. He hopes to do an honours degree next year, researching into optimal control theory and extensions of variational calculus into non-homogeneous spaces. Stephen wishes to gain entrance into medicine so that he may put his problem-solving skills to use in real-life situations where people are in need of help.
Classical Problems in Calculus of Variations and Optimal Control
The aim of my project is to develop significant expertise in techniques used to study abnormal extremals in the calculus of variations and optimal control theory. The first part of the project will be to understand and outline selected variational problems and generate the differential equations for their solutions. These classical problems pose very interesting questions that require investigation. The second part of this project will be to investigate methods of solving these differential equations, in the attempt to obtain numerical solutions to the problems.
The research component is to explore extensions of classical problems to variational problems for curves in Riemannian, then sub-Riemannian, geometry. This project will help build a strong framework for further research at a postgraduate level.