On a Class of Optimal Control Problems for Functional Differential Systems

Abstract

A linear functional differential control system of general form with aftereffect is considered. An optimal control problem with linear constraints on the state and control variables is studied. The control is realized by a linear operator of general form. The cases of distributed and lumped delay in the control loop, as well as the case of impulsive control, are covered. The Cauchy matrix is used to reduce the problem under consideration to a problem formulated only in terms of control variables with the use of some auxiliary variables linked with the defining relations for the Cauchy matrix of the system. In the case where the control is chosen from a finite-dimensional subspace of the control space, a problem effectively solvable by standard software tools is written explicitly. An example of an applied optimal control problem that arises in economic dynamics is presented. A class of hybrid systems (systems with continuous and discrete times) reducible to the system under consideration is described.