### Details

#### Title

The problem of control of rod heating process with nonseparated conditions at intermediate moments of time#### Journal title

Archives of Control Sciences#### Affiliation

Barseghyan, Vanya R. : Institute of Mechanics of the National Academyof Sciences of Armenia, Yerevan State University, Armenia#### Authors

#### Keywords

heating control ; temperature ; intermediate moments of time ; nonseparated multipoint conditions ; complete controllability#### Divisions of PAS

Nauki Techniczne#### Coverage

481-493#### Publisher

Committee of Automatic Control and Robotics PAS#### Bibliography

[1] A.G. Butkovskii: Control Methods for Systems with Distributed Parameters. Nauka, 1975 (in Russian).[2] A.G Butkovskii, S.A Malyi, and Yu.N. Andreev: Optimal Control of Metal Heating. Moscow, Metallurgy, 1972 (in Russian).

[3] A.I. Egorov: Optimal Control of Thermal and Diffusion Processes. Nauka, 1978 (in Russian).

[4] A.I. Egorov and L.N. Znamenskaya: Introduction to the Theory of Control of Systems with Distributed Parameters. Textbook, Saint Petersburg, LAN, 2017 (in Russian).

[5] E.Ya. Rapoport: Structural Modeling of Objects and Control Systems with Distributed Parameters. Higher School, 2003 (in Russian).

[6] A.N. Tikhonov and A.A. Samarskii: Equations of Mathematical Physics. Nauka, 1977 (in Russian).

[7] V.I. Ukhobotov and I.V. Izmest’ev: A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source. Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 25(1), (2019), 297–305 (in Russian), DOI: 10.21538/0134-4889-2019-25-1-297-305.

[8] V.I. Ukhobotov and I.V. Izmest’ev: The problem of controlling the process of heating the rod in the presence of disturbance and uncertainty. IFAC Papers OnLine, 51(32), (2018), 739–742, DOI: 10.1016/j.ifacol.2018.11.458.

[9] V.I. Butyrin and L.A. Fylshtynskyi: Optimal control of the temperature field in the rod when changing the control zone programmatically. Applied Mechanics, 12(84), (1976), 115–118 (in Russian).

[10] M.M. Kopets: Optimal control over the process of heating of a thin core. Reports of the National Academy of Sciences of Ukraine, 7, (2014), 48–52 (in Ukrainian), http://dspace.nbuv.gov.ua/handle/123456789/87951.

[11] N.V.Gybkina, D.Yu. Podusov, and M.V. Sidorov: The optimal control of a homogeneous rod final temperature state. Radioelectronics and Informatics, 2 (2014), 9–15 (in Russian).

[12] E.Y. Vedernikova and A.A. Kornev: To the problem of rod heating. Moscow Univ. Math. Bull., 69, (2014), 237–241, DOI: 10.3103/S0027132214060023.

[13] J.F. Bonnans and P. Jaisson: Optimal control of a parabolic equation with time-dependent state constraints. SIAM Journal on Control and Optimization, 48(7), (2010), 4550–4571.

[14] A. Lapin and E. Laitinen: Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation. Journal of Applied Mathematics and Physics, 6, (2018), 58–68, DOI: 10.4236/jamp.2018.61007.

[15] K. Kunisch and L. Wang: Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 19(2), (2013), 460–485, http://eudml.org/doc/272753.

[16] J.M. Lemos, L. Marreiro, and B. Costa: Supervised multiple model adaptive control of a heating fan. Archives of Control Sciences, 18(1), (2008), 5–16.

[17] S.H. Jilavyan, E.R. Grigoryan, and A.Zh. Khurshudyan: Heating control of a finite rod with a mobile source. Archives of Control Sciences, 31(2), (2021), 417–430, DOI: 10.24425/acs.2021.137425.

[18] V.R. Barseghyan: Control problem of string vibrations with inseparable multipoint conditions at intermediate points in time. Mechanics of Solids, 54(8), (2019), 1216–1226. DOI: 10.3103/S0025654419080120.

[19] V.R. Barseghyan: Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants. Automation and Remote Control, 81(2), (2020), 226–235, DOI: 10.1134/S0005117920020034.

[20] V.R. Barseghyan: Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Nauka, 2016 (in Russian).

[21] V.R. Barseghyan and T.V. Barseghyan: On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions. Automation and Remote Control, 76(4), (2015), 549–559, DOI: 10.1134/S0005117915040013.