On the degeneracy phenomenon for nonlinear optimal control problems with higher-index state constraints

Necessary conditions of optimality (NCO) play an important role in optimization problems. They are the major tool to select a set of candi-dates to minimizers. In optimal control theory, the NCO appear in the form of a Maximum Principle (MP). For certain optimal control prob-lems with state constraints, it might happen that the MP are unable to provide useful information — the set of all admissible solutions coincides with the set of candidates that satisfy the MP. When this happens, the MP is said to degenerate. In the recent years, there has been some lit-erature on fortified forms of the MP in such way that avoid degeneracy. These fortified forms involve additional hypotheses — Constraint Qualifi-cations. Whenever the state constraints have higher index (i.e. their first derivative with respect to time does not depend on control), the current constraint qualifications are not adequate. So, the main purpose here is fortify the maximum principle for optimal control problems with higher index constraints, for which there is a need to develop new constraint qualifications. The results presented here are a generalization of [Fon05] by allowing nonlinear problems