Mathematics

Solving the optimal control problem for one stochastic non-stationary Leontief model

M. A. Sagadeeva, D. F. Abyzgareev

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article considers the construction for optimal control of solutions for a stochastic non-stationary Leontief type system. The non-stationarity of the system is taken in some averaged form and taken out as a multiplier in the right part of the operator-differential equation with a degenerate matrix of coefficients at the derivative. At the same time, the stochastic component is assumed in the initial condition. Using the linearity of the system under consideration, we split it into a deterministic and a stochastic problem. Next, based on the algorithms obtained earlier for the deterministic non-stationary problem, we find the optimal control. The article aims to describe a computational experiment that illustrates the results on the solvability of this problem. In addition to the introduction, the conclusion and the list of references, the article consists of two parts. The first part provides information on the solvability of the problem, while the second part presents the results of the computational experiment.

Keywords: Leontief type equations, Nelson–Glickikh derivative, space of differentiable “noises”, computational experiment.

UDC: 517.9

Received: 08.10.2025

DOI: 10.14529/mmph250405