Dynamic programming for impulse controls

This paper describes the theory of feedback control in the class of inputs which allow delta-functions and their derivatives. It indicates a modification of dynamic programming techniques appropriate for such problems. Introduced are physically realizable bang-bang-type approximations of the “ideal” impulse-type solutions. These may also serve as “fast” feedback controls which solve the terminal control problem in arbitrary small time. Examples of damping high-order oscillations in finite time are presented.