ON THE CONSTRUCTION OF PROGRAM CONTROL IN THE PROBLEM ON ATTAINABLE VALUES OF ON-TARGET FUNCTIONALS FOR DYNAMIC ECONOMIC MODELS WITH DISCRETE MEMORY

Abstract

Main constructions and relationships for program control actions are proposed as applied to the problem on attainable prescribed values of on-target functionals for continuous-discrete dynamic economic mathematical model with discrete memory under given polyhedral constrains with respect to control. The form of on-target functionals covers widely used kinds of functionals such as multipoint, integral ones and linear combinations of those. The feature of the control system under consideration is the presence of two kinds of the state variables, namely, a part of them depends on continues time, whereas others depend on discrete time. Aftereffect of the system is defined by its discrete memory located at a given collection of instants. The results are obtained on the basis of the principal statements from the general theory of continuous-discrete systems. In the constructive part of the research, the basic idea is the reduction of the original problem to a variant of the general moment problem with taking into account pointwise polyhedral constraints on controls. This allows us to construct estimates of the attainability set and to build program controls on the base of solutions to a series of linear programming problems. Every such a problem provides us with values of the program control on a partial segment. All these values are used while constructing the program control as a whole. The mentioned procedures use in essence the Cauchy operator to the hybrid system under consideration. The property of this operator are studied in the cited previous papers. The obtained results constitute an instrumental basis for efficient studying and constructing solutions to urgent applied problems with constrained resources of control.