Pontryagin's maximum principle for optimal impulsive control problems

A necessary optimality conditions in the form of Pontryagin's maximum principle for an impulsive control problem with mixed constraints has been reported. A new concept of an impulsive control is proposed that generalizes previously known ones and makes it possible to control the trajectory of a system at its jumps. The maximum principle is obtained under relaxed regularity assumptions for mixed constraints. The basic difference of the problem in question from those studied by other authors is that the dynamical system can be controlled at jumps in its phase trajectory caused by the presence of impulses. The regularity assumptions for mixed constraints are relaxed in comparison with the traditional assumptions.