Nondegeneracy and normality in necessary conditions involving Hamiltonian inclusions for state-constrained optimal control problems

Similarly to other standard versions of the maximum principle, recently derived necessary conditions of optimality involving Hamiltonian inclusions are satisfied by a degenerate set of multipliers when applied to problems to which the initial state is fixed and it is in the boundary of the state constraint set. In such case, the necessary conditions do not provide useful information to select minimizers. A constraint qualification under which nondegenerate necessary conditions based on a "standard" maximum principle was previously defined. In this paper we show that when the "velocity set" is convex the same constraint qualification permits nondegenerate necessary conditions involving Hamiltonian inclusions. This is of relevance since it covers problems in which the set of multipliers produced by Hamiltonian inclusion conditions is smaller than those generated by "standard" maximum principles. Furthermore, we show that the constraint qualification can be strengthened so that normality can be established.