An Integral-type Constraint Qualification for Optimal Control Problems with State Constraints ∗

Standard necessary conditions of optimality (NCO) for constrained optimal control problems – Maximum Principle type conditions – may fail to provide useful information to select candidates to minimizers among the overall set of admissible solutions. This phenomenon is known as the degeneracy phenomenon and there has been continuing interest in the literature in 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, can be verified for more problems.