Multiobjective optimal control problems with endpoint and state constraints

In this thesis we consider nonsmooth multiobjective optimal control problems in terms of a general preference on $Rm$. The optimal control problems considered involve differential inclusion, endpoint constraints and state constraints. 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 is 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.