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

This paper concerns the investigation of a general impulsive con-trol problem. The considered impulsive processes are of non-standard type: control processes admit ordinary type controls as the impulse develops. New necessary conditions of optimality in the form of Pontryagin Maximum Principle are obtained. These conditions are applied to a model problem and are shown to yield useful information about optimal control modes.