Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster

Authors

DOI:

https://doi.org/10.15587/1729-4061.2022.252866

Keywords:

optimal control problem, three-sector economic cluster, Lagrange multiplier method, nonlinear system, quadratic functional

Abstract

The problem of optimal control over a finite time interval for a mathematical model of a three-sector economic cluster is posed. The economic system is reduced by means of transformations to the optimal control problem for one class of nonlinear systems with coefficients depending on the state of the control object. Two optimal control problems for one class of nonlinear systems with and without control constraints are considered. The nonlinear objective functional in these problems depends on the control and state of the object. Then, using the results of solving optimal control problems on a finite interval, an algorithm for solving the problem for a nonlinear system of a three-sector economic cluster is developed. A nonlinear control based on the feedback principle using Lagrange multipliers of a special kind is found. The results obtained for nonlinear systems are used to construct the control parameters of a mathematical model of a three-sector economic cluster at a finite time interval with a given functional and various initial conditions. The results of the system state calculation are shown in the figures, the optimal controls satisfy the given constraints. The optimal distribution of labor and investment resources for a three-sector economic cluster is determined. They ensure that the system is brought into an equilibrium state and satisfy balance ratios. These results are useful for practice and are important because there are a number of optimal control problems when it is necessary to transfer a system from an initial state to a desired final state for a given time interval. Such problems often arise for an economic system when a certain level of development is required.

Author Biographies

Zainelkhriet Murzabekov, Al-Farabi Kazakh National University

Doctor of Technical Sciences, Professor

Department of Artificial Intelligence and Big Data

Marek Milosz, Lublin University of Technology

PhD, Professor, Head of Department, Head of Laboratory

Department of Software Engineering and Database Systems

Laboratory of Motion Analysis and Interface Ergonomics

Kamshat Tussupova, Al-Farabi Kazakh National University

PhD, Senior Lecturer

Department of Information Systems

Gulbanu Mirzakhmedova, Al-Farabi Kazakh National University

Master of MCM, Senior Lecturer

Department of Information Systems

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Published

2022-02-28

How to Cite

Murzabekov, Z., Milosz, M., Tussupova, K., & Mirzakhmedova, G. (2022). Development of an algorithm for solving the problem of optimal control on a finite interval for a nonlinear system of a three-sector economic cluster. Eastern-European Journal of Enterprise Technologies, 1(3(115), 43–52. https://doi.org/10.15587/1729-4061.2022.252866

Issue

Vol. 1 No. 3(115) (2022): Control processes

Section

Control processes

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Copyright (c) 2022 Zainelkhriet Murzabekov, Marek Milosz, Kamshat Tussupova, Gulbanu Mirzakhmedova

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