Nondegenerate necessary conditions for optimal control problem with state constraints: Integral-type constraint qualification

The main purpose of necessary conditions of optimality (NCO) is to identify a `small´ set of candidates to minimizers among the overall set of admissible solutions. However, for certain optimal control problems with state constraints, it might happen that the set of all admissible solutions coincides with the set of candidates satisfying the NCO. This phenomenon is known as the degeneracy phenomenon and there has been some literature proposing stronger forms of NCO that can be informative in such cases: the so-called nondegenerate NCO. The nondegenerate NCO proposed here are valid under a different set of hypothesis and under a constraint qualification of an integral-type that, in relation to some previous literature, is easier to verify.