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 fi rst 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 refi ned 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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