Title page for ETD etd-10022010-115320


Type of Document Dissertation
Author Barnard, Richard Charles
Author's Email Address rbarna2@lsu.edu, richard.c.barnard@gmail.com
URN etd-10022010-115320
Title Hamilton-Jacobi Theory for Optimal Control Problems on Stratified Domains
Degree Doctor of Philosophy (Ph.D.)
Department Mathematics
Advisory Committee
Advisor Name Title
Wolenski, Peter Committee Chair
Bourdin, Blaise Committee Member
Lawson, Jimmie Committee Member
Neubrander, Frank Committee Member
Perlis, Robert Committee Member
Kundu, Sukhamay Dean's Representative
Keywords
  • nonsmooth analysis
  • stratified domains
  • Hamilton-Jacobi
  • proximal normal
  • invariance
  • Mayer problem
  • value function
Date of Defense 2010-09-24
Availability unrestricted
Abstract
This thesis studies optimal control problems on stratified domains. We first establish a known proximal Hamilton-Jacobi characterization of the value function for problems with Lipschitz dynamics. This background gives the motivation for our results for systems over stratified domains, which is a system with non-Lipschitz dynamics that were introduced by Bressan and Hong. We provide an example that shows their attempt to derive a Hamilton-Jacobi characterization of the value function is incorrect, and discuss the nature of their error. A new construction of a multifunction is introduced that possesses properties similar to those of a Lipschitz multifunction, and is used to establish Hamiltonian criteria for weak and strong invariance. Finally, we use these characterizations to show that the minimal time function and the value function for a Mayer problem, both over stratified domains, satisfy and are the unique solutions to a proximal Hamilton-Jacobi equation.
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