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
Murzabekov Z. Milosz M. Tussupova K. Mirzakhmedova G.
2022Technology Center
Eastern-European Journal of Enterprise Technologies
2022#1Issue 3-11543 - 52 pp.
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
Lagrange multiplier method , Nonlinear system , Optimal control problem , Quadratic functional , Three-sec-tor economic cluster
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Department of Artificial Intelligence and Big Data, Department of Information Systems, Al-Farabi Kazakh National University, Al-Farabi ave.71, Almaty, 050040, Kazakhstan
Department of Software Engineering and Database Systems, Laboratory of Motion Analysis and Interface Ergonomics, Lublin University of Technology, Nadbystrzycka str,38 D, Lublin, 20–618, Poland
Senior Lecturer, Department of Information Systems, Al-Farabi Kazakh National University, Al-Farabi ave.,71, Almaty, 050040, Kazakhstan
Department of Information Systems, Al-Farabi Kazakh National University, Al-Farabi ave.,71, Almaty, 050040, Kazakhstan
Department of Artificial Intelligence and Big Data
Department of Software Engineering and Database Systems
Senior Lecturer
Department of Information Systems
10 лет помогаем публиковать статьи Международный издатель
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