Some recent developments in necessary conditions of optimality for impulsive control problems

Abstract

Necessary conditions of optimality for impulsive control systems whose dynamics are defined by differential inclusions and whose state trajectory is subject to state constraints endpoint constraints are discussed. After discussing the motivation of this general control paradigm in the context of space systems, a natural concept of robust solution is introduced and some of his properties presented. Besides an independent interest for the construction of schemes approximating impulsive con- trol processes by conventional ones, it is shown in a brief outline of the proof how these properties play an important role in the derivation of the considered optimal- ity conditions. Finally, the relation between these conditions and the ones recently developed in the context of the considered solution concept.