On constraint qualifications for nondegenerate necessary conditions of optimality applied to optimal control problems

Abstract

We address necessary conditions of optimality (NCO), in the form ofa maximum principle, for optimal control problems with stateconstraints. In particular, we are interested in the NCO that arestrengthened to avoid the degeneracy phenomenon that occurs when thetrajectory hits the boundary of the state constraint.In the literature on this subject, we can distinguish two types ofconstraint qualifications (CQ) under which the strengthened NCO canbe applied: CQ involving the optimal control and CQ not involvingit. Each one of these types of CQ has its own merits. The CQs involving the optimal control are not so easy to verify, but, are typically applicable to problems with less regularity on the data. In this article, we provide conditions under which the type of CQ involving the optimal control can be reduced to the other type. In this way, we also provide nondegenerate NCO that are valid under a different set of hypotheses.