Properties of the attainability set of a dynamic system with impulsive control (Q1914107)

A nonlinear control system with impulsive integrally bounded control is considered. It is shown that the attainable set is compact and continuously dependent with respect to parameters and resource of controls. As a corollary, it is obtained that the extremal value of a terminal functional of an optimal control impulse problem depends also in a continuous way on the perturbations of parameters and resource of control. For a particular case of bilinear systems, the number of control pulses, needed to transfer the phase point of the system from its initial position to a given point of the attainable set, is estimated.