Critical cones for regular controls with inequality constraints

Based on the notions of normality and regularity for constrained problems in optimization, a conjecture on second order necessary conditions related to different critical cones is posed for a wide range of optimal control problems involving equality and inequality constraints. Several properties of the sets and functions delimiting the problem are derived and, for a specific case where the surmise has been proved correct, some fundamental questions derived from this result are completely solved. Mathematics Subject Classification: 49K15