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Russia Chelyabinsk
Section Mathematics
Title Numerical solution of a control problem for a parabolic system with disturbances
Author(-s) Izmest'ev I.V.ab, Ukhobotov V.I.ab, Kudryavtsev K.N.ab
Affiliations Chelyabinsk State Universitya, South Ural State Universityb
Abstract A controlled parabolic system that describes the heating of a given number of rods is considered. The density functions of the internal heat sources of the rods are not known exactly, and only the segments of their change are given. At the ends of the rods there are controlled heat sources and disturbances. The goal of the choice of control is to lead the vector of average temperatures of the rods at a fixed time to a given compact for any admissible functions of the density of internal heat sources and any admissible realizations of disturbances. After replacing variables, the problem of controlling a system of ordinary differential equations in the presence of uncertainty is obtained. Using a numerical method, a solvability set is constructed for this problem. Model calculations are carried out.
Keywords control, disturbance, parabolic system
UDC 517.977
MSC 35K05, 49N70, 91A23
DOI 10.35634/vm240103
Received 25 November 2023
Language English
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