标题：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
期刊名称：Eastern-European Journal of Enterprise Technologies
印刷版ISSN：1729-3774
电子版ISSN：1729-4061
出版年度：2022
卷号：1
期号：3
页码：43-52
DOI：10.15587/1729-4061.2022.252866
语种：English
出版社：PC Technology Center
摘要：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.
关键词：optimal control problem;three-sector economic cluster;Lagrange multiplier method;nonlinear system;quadratic functional
