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Russia Chelyabinsk; Yekaterinburg
Year
2022
Volume
32
Issue
4
Pages
546-556
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Section Mathematics
Title On one problem of controlling the heating of a rod system under uncertainty
Author(-s) Izmest'ev I.V.ab, Ukhobotov V.I.ab
Affiliations Chelyabinsk State Universitya, Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesb
Abstract The problem of control of a parabolic system, which describes the heating of a given number of rods, is considered. The density functions of the internal heat sources of the rods are not exactly known, and only the segment of their change is given. Control are point heat sources that are located at the ends of the rods. The goal of the choice of control is to ensure that at a fixed time the modulus of the linear function determined using the average temperatures of the rods does not exceed the given value for any admissible functions of the density of internal heat sources. A technique has been developed for reducing this problem to a one-dimensional control problem under uncertainty. Necessary and sufficient termination conditions are found.
Keywords control, uncertainty, parabolic system
UDC 517.977
MSC 35K05, 49N70, 91A23
DOI 10.35634/vm220404
Received 18 November 2022
Language Russian
Citation Izmest'ev I.V., Ukhobotov V.I. On one problem of controlling the heating of a rod system under uncertainty, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 546-556.
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