First order conditions under state constraints***This position has been filled***

• Location: Université Pierre et Marie Curie, Paris 6

• Secondment: Imperial College – London

• Application deadline:  October 31, 2011
• Advisor: Helene Frankowska
• Contacts: Helene Frankowska

 The Pontryagin Maximum Principle (PMP) is said to be normal when the cost multiplier is nonzero. A normal version of the PMP is the starting point for deriving higher order necessary conditions, for deriving certain kinds of sufficient conditions and for establishing regularity properties of optimal controls. It is therefore important to establish normality of the PMP under general conditions. Existing conditions of normality of the PMP for problems with state constraints are very restrictive. They do not cover situations when both endpoints of state trajectories are constrained, and apply only to rather special kinds of state constraint representations. The aim is to establish normality in more general situations, when both state trajectory endpoints are constrained and when current restrictions on the nature of the pathwise state constraints are removed.

The fellowship is composed of 12 months research  at UPMC and 6 months at the Imperial College.