Acceptable area of optimal control for a multidimensional system

TL;DR

This paper analyzes the phase space of multidimensional systems with multiple subsystems, proposing a control loop approach to optimize control regions and demonstrating significant improvements in objective function values and regional economic growth.

Contribution

It introduces a method to determine the dynamic control region in multidimensional systems and shows how optimal control can significantly enhance economic outcomes.

Findings

Optimal control increases objective function value by 85% over 5 years.

Resource distribution can be optimized to boost regional GDP from 2% to 7-8%.

Control loop approach effectively manages complex multidimensional systems.

Abstract

A research shows the phase space of the system. The phase space of such a system is determined by the development structure of four subsystems with different objective functions. The control loop of such a system is formed. Using the control loop, optimal control is generated. The dynamic control region is calculated on the basis of a matrix determining the structure of the development of a multidimensional dynamic system. It was established that the optimal distribution by R. Bellman's method allows increasing the increase in the value of the objective function over 5 years by 85% from the initial value with a decrease in the distributed resource by 20%. It is believed that the construction of railways leads to an increase in gross regional product by 2%, but the authors proved that it is possible to increase this figure to 7-8%