On a generalization of the impulsive control concept:Controlling system jumps

This paper concerns the investigation of a general impulsivecontrol problem. The considered impulsive processes are ofnon-standard type: control processes admit ordinary type controlsas the impulse develops. New necessary conditions of optimality inthe form of Pontryagin Maximum Principle are obtained. Theseconditions are applied to a model problem and are shown to yielduseful information about optimal control modes.