Second order necessary conditions of optimality for impulsive control problems

In this article, we present first and second order conditions for an impulsive optimal control problem. Although far from being the most general one to which the adopted approach can be applied, it is sufficiently rich to illustrate the power of our methods. After a detailed description of the considered impulsive optimal control problem, the first and second order necessary conditions of optimality are stated. Finally, an outline of the proof is presented with some conclusions.