Investigation of variable structure optimal control problems is one of the important directions of the optimal control theory. Change of the structure of a system means that the system at some beforehand unknown moment may go over from one law of movement to another. Moreover, after changing the structure the initial condition of the system depends on its previous state. This joins them into a single system with variable structure. Such problems are important for various practical applications.
In this article we consider the general economic system, the main purpose of which is to meet all the basic needs of society. Important features of the economic system are described. The classification of the economic system according to the ability to meet the main goal is given. It also takes into account the fact that the essence of the economic system depends on the political system in society, which is constant at certain intervals of time, but can change at any time unknown in advance. This feature of the economic-political system allows us to consider this system as a variable structure optimal control system.
We introduce indicators of efficiency and effectiveness of the economic system, which give us information about the state of the economic system at a given time interval and at a given point in time, respectively. Based on the performed analysis, three types of tasks for optimal management of the economic system are posed. One simple linear variable structure economic-political system optimal control problem is presented for illustration.

Keywords: variable structure, control problem, economic system, political system, effectiveness of the economic system, system efficiency, optimal management.
JEL Codes: P10, P40, P51, P52

Introduction

Economic-political system is unity of possibility complex actions, which provides all the basic public service needs satisfaction in every time moment from a given time interval. Society’s production is mainly involved in the governance of the existing material and labor resources. In addition, the economic system depends on the essence of the current political system, which is constant at the given time interval. All of them received from the general economic-political system. Obviously, the economic-political system has a cyclical nature and is conjugate with the time interval (cycle). Therefore, it provides information about the weaknesses of the economic-political system only at the end of the cycle. The economic-political system of some nature at the time interval may have a tendency to change its nature. We assume that the political system can be of three types: the first - the unsatisfactory, the second – transitional or the neutral, and the the third - the overly satisfying. Take into consideration the change in the political system, the optimal control problem will take the form of a variable-structure optimal control problem.

Statement of the problem

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