On pulse optimal control of linear systems with aftereffect

The paper deals with the problem of pulse optimal control of a linear dynamic system with aftereffect. As a functional, the degenerate quadratic functional of the most common kind is considered. The absence of control in the functional leads to the fact that the optimal control contains a pulse component. Sufficient conditions of existence of the pulse optimal control are obtained and the equations describing coefficients in the optimal control are worked out. Sufficient conditions that make it possible to integrate equations and to find the coefficients in an explicit form for the optimal control are established. A model example is considered.