Second-order necessary conditions for optimal impulsive control

Second-order conditions of optimality for an impulsive control problem are presented and derived from those for an appropriate abstract optimization problem with equality, inequality and set inclusion constraints. An important feature of these conditions is that they do not degenerate for abnormal control processes in spite of the absence of a priori normality assumptions on the data of the problem. Another salient feature concerns the fact that these conditions improve previous results by taking into account the second-order curvature effect of the constraints in the form of inclusion. Copyright © 2005 IFAC.