Type of Document Dissertation Author Huang, Lingyan Author's Email Address firstname.lastname@example.org URN etd-11142012-144831 Title Subgradient Formulas for Optimal Control Problems with Constant Dynamics Degree Doctor of Philosophy (Ph.D.) Department Mathematics Advisory Committee
Advisor Name Title Wolenski, Peter Committee Chair Adkins, William Committee Member Lawson, Jimmie Committee Member Litherland, Richard A Committee Member Shipman, Stephen Committee Member Peng, Lu Dean's Representative Keywords
- variational analysis and optimization
- Hamilton-Jacobi equation
- Minkowski gauges
- normal cones
- minimal time function
Date of Defense 2012-11-08 Availability unrestricted AbstractIn this thesis our first concern is the study of the minimal time function corresponding
to control problems with constant convex dynamics and closed target sets.
Unlike previous work in this area, we do not make any nonempty interior or calmness
assumptions and the minimal time functions is generally non-Lipschitzian.
We show that the Proximal and Fréchet subgradients of the minimal time function
are computed in terms of normal vectors to level sets. And we also computed the
subgradients of the minimal time function in terms of the F-projection.
Secondly, we consider the value function for Bolza Problem in optimal control
and the calculus of variations. The main results present refined formulas for calculating
the Fréchet subgradient of the value function under minimal requirements,
and are similar to those obtained for the minimal time function.
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