Second order necessary conditions of optimality for impulsive control systems

Second order conditions of optimality are presented for an impulsive control problem. The general approach defined in order to derive informative optimality conditions allows the consideration of abnormal problems without additional assumptions. 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, which is based in the extremal principle, is presented with some conclusions.