Title page for ETD etd-11142012-144831

Type of Document

Dissertation

Author

Huang, Lingyan

Author's Email Address

lhuan12@lsu.edu

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
subdifferentials
Minkowski gauges
normal cones
minimal time function

Date of Defense

2012-11-08

Availability

unrestricted

Abstract

In 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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