Second order necessary conditions for optimal impulsive control problems

First and second order necessary conditions of optimality for an impulsive control problem are presented and derived. One of the main features of these results is that no a priori normality assumptions are required and they are informative for abnormal control processes as well. This feature follows from the fact that the conditions are derived from an extremal principle, which is proved for an abstract minimization problem with equality and inequality type constraints and constraints given by convex cone.