Variable Structure Optimal Control Problem for the Economic-Political Systems with Continuous Intermediate Conditions

TL;DR: Variable structure optimal control problem for the economic-political systems with continuous intermediate conditions investigates the optimal control of systems with variable structure, where the system structure changes over time and the initial condition depends on the previous state of the system.

Abstract: 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. 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 with continuous intermediate conditions. 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. 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.