Abstract:
A control problem is considered for the process of heating a rod by varying the temperature at its left end. The exact values of the temperature at the right end of the rod and the heat density function are unknown; only the ranges of their possible values are given. The aim of the control is to ensure that the average temperature of the rod at a fixed time belongs to a given interval. We find necessary and sufficient conditions on the initial temperature of the rod under which the aim of the control can be achieved for any admissible unknown functions. The corresponding heating control at the left end of the rod is constructed.
Citation:
V. I. Ukhobotov, I. V. Izmestyev, “A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 1, 2019, 297–305
\Bibitem{UkhIzm19}
\by V.~I.~Ukhobotov, I.~V.~Izmestyev
\paper A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 1
\pages 297--305
\mathnet{http://mi.mathnet.ru/timm1617}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-1-297-305}
\elib{https://elibrary.ru/item.asp?id=37051112}
Linking options:
https://www.mathnet.ru/eng/timm1617
https://www.mathnet.ru/eng/timm/v25/i1/p297
This publication is cited in the following 9 articles:
I. V. Izmestyev, V. I. Ukhobotov, K. N. Kudryavtsev, “Numerical solution of a control problem for a parabolic system with disturbances”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:1 (2024), 33–47
I. V. Izmestev, N. D. Livanov, “Zadacha upravleniya parabolicheskoi sistemoi s pomekhami i vozmozhnymi izmeneniyami v dinamike”, Izv. IMI UdGU, 64 (2024), 34–47
I. V. Izmestev, V. I. Ukhobotov, “Zadacha upravleniya parabolicheskoi sistemoi s pomekhami i vypukloi tselyu”, Izv. IMI UdGU, 62 (2023), 30–42
Igor' V. Izmest'ev, Viktor I. Ukhobotov, “Control problem for a parabolic system with uncertainties and a non-convex goal”, Ural Math. J., 9:2 (2023), 121–131
I. V. Izmestev, V. I. Ukhobotov, “Ob odnoi zadache upravleniya nagrevom sistemy sterzhnei pri nalichii neopredelennosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:4 (2022), 546–556
V. I. Ukhobotov, I. V. Izmestev, “Ob odnoi zadache upravleniya protsessom ochistki vodoema ot primesi”, Izv. IMI UdGU, 57 (2021), 181–189
V. R. Barseghyan, “The problem of control of rod heating process with nonseparated conditions at intermediate moments of time”, Arch. Control Sci., 31:3 (2021), 481–493
A. S. Sushkov, “Upravlenie protsessom nagreva sterzhnya v dvizhuscheisya srede
s ob'emnym teplovydeleniem”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 427–438
Elena Tabarintseva, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 578
Citation in format AMSBIB
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