Abstract
Consideration was given to a class of the problems of optimal control of rod (plate) heating by controlling the furnace temperature. Control relies on the process information feedbacked continuously or discretely only from the individual points on the rod where the temperature sensors are installed. For the continuous and discrete observation, the mathematical model of the controlled process was reduced to the pointwise loaded parabolic equation. The paper established formulas for the functional gradient, proposed schemes of their numerical solution, and presented the results of the numerical experiments.
Similar content being viewed by others
References
Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control and Optimization, Heidelberg: Springer, 1992.
The Control Handbook, Levine, W.S., Ed., Boca Raton: CRC Press, 1996, pp. 895–908.
Vasil’ev, F.P., Metody optimizatsii (Methods of Optimization), Moscow: Faktorial Press, 2002.
Egorov, A.I., Osnovy teorii upravleniya (Introduction to the Control Theory), Moscow: Fizmatlit, 2004.
Ray, W.H., Advanced Process Control, New York: McGraw-Hill, 1981.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Butkovskii, A.G., Metody upravleniya sistemami s raspredelennymi parametrami (Distributed-parameter Systems: Methods of Control), Moscow: Nauka, 1984.
Sergienko, I.V. and Deineka, V.S., Optimal Control of Distributed Systems with Conjugation Conditions, New York: Kluwer, 2005.
Aida-zade, K.R., An Approach to the Design of the Lumped Control in Distributed Systems, Avtomat. Vychisl. Tekhn., 2005, no. 3, pp. 16–22.
Nakhushev, A.M., Zadachi so smesheniem dlya uravnenii v chastnykh proizvodnykh (Problems with Mixing for the Partial Derivative Equations), Moscow: Nauka, 2005.
Nakhushev, A.M., Uravneniya matematicheskoi biologii (Equations of Mathematical Biology), Moscow: Vysshaya Shkola, 1995.
Alikhanov, A.A., Berezkov, A.M., and Shkhanukov-Lafshiev, M.Kh., Boundary Problems for Some Classes of Loaded Differential Equations and Difference Methods for Their Numerical Realization, Zh. Vychisl. Mat. Mat. Fiz., 2008, vol. 48, no. 9, pp. 1619–1628.
Aida-zade, K.R., On Numerical Solution of the Differential Equation Systems with Nonlocal Conditions, Vychisl. Tekhnol., 2004, vol. 9, no. 1, pp. 11–25.
Abdullaev, V.M. and Aida-zade, K.R., Numerical Solution of the Problem of Optimal Control of the Loaded Lumped Systems, Zh. Vychisl. Mat. Mat. Fiz., 2006, vol. 46, no. 9, pp. 1566–1581.
Abdullaev, V.M. and Aida-zade, K.R., On Numerical Solution of the Loaded Systems of the Ordinary Differential Equations, Zh. Vychisl. Mat. Mat. Fiz., 2004, vol. 44, no. 9, pp. 1585–1595.
Tikhonov, A.N. and Samarskii, A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1966.
Lions, J.L., Controle optimal des systèmes gouvernés par des équations aux derivées partielles, Paris: Dunod Gauthier-Villars, 1968. Translated under the title Optimal’noe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Moscow: Mir, 1972.
Evtushenko, Yu.G., Metody resheniya ekstremal’nykh zadach i ikh primenenie v sistemakh optimizatsii (Methods for Solution of the Extremal Problems and Their Use in the Optimization Systems), Moscow: Nauka, 1982.
Abdullaev, V.M., On Using the Method of Lines for the Boundary Problem Nonlocal Conditions Relative to the Loaded Parabolic Equation, Izv. Nat. Akad. Nauk Azerb., Ser. FTMN, 2008, vol. 28, no. 3, pp. 76–81.
Author information
Authors and Affiliations
Additional information
Original Russian Text © K.R. Aida-zade, V.M. Abdullaev, 2012, published in Avtomatika i Telemekhanika, 2012, No. 9, pp. 3–19.
Rights and permissions
About this article
Cite this article
Aida-zade, K.R., Abdullaev, V.M. On an approach to designing control of the distributed-parameter processes. Autom Remote Control 73, 1443–1455 (2012). https://doi.org/10.1134/S0005117912090019
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117912090019