Kirsty J. Eisenhart
Doctor of Philosophy
Title: Multiobjective Optimal Control Problems with Endpoint
and State Constraints
Dr. Qiji (Jim) Zhu, Chair
Dr. Jay Treiman
Dr. Yuri Ledyaev
Dr. Terrell Hodge
Dr. Boris Mordukhovich
Date: Wednesday, March 19, 2003, 10:00 a.m. - 12:00 p.m.
6625 Everett Tower
In this Theses we consider nonsmooth multiobjective optimal
control problems in terms of general preference on Rm . The optimal
control problems considered involve differential inclusion, endpoint
constraints and state constraint. No convexity assumption is needed
on the differential inclusion. Examples of common preferences are given,
and the idea of approximating a preference is introduced. Euler-Lagrange
necessary conditions and a form of the maximum principle are developed
for closed preferences (and those that can be approximated by closed
preferences) in terms of the limiting subdifferential. As a consequence,
this sis the first result in the literature for Lexicographical order.
Also this is the first time noncontinuous utility functions are considered.
A transversality condition in terms of the limit supremum of normal
cones to the level sets of the preference is also developed.
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