Geodesic
Real-time optimal control of a special distributed parameter system
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 12, pp. 1839-1850 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of constructing positional solutions under the real-time optimal control of a parabolic system is considered. A method for finding an approximate solution of the problem is justified. According to the method, the problem is reduced to the optimal control problem for a large dynamical ordinary differential system, which is solved by applying a dynamical version of the dual linear programming method. The fundamental matrix of the homogeneous part of the system is quasi-decomposed to save computation time at the iterations of the method. An optimal controller is described whereby the current optimal feedback values (positional solution) are constructed in real time. Numerical results are presented for the control of thermal processes in a rod. 
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R. Gabasov; F. M. Kirillova; D. S. Kuzmenkov. Real-time optimal control of a special distributed parameter system. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 12, pp. 1839-1850. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_12_a1/

[1] Butkovskii A. G., Metody upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1975

[2] Vasilev F. P., Lektsii po metodam resheniya ekstremalnykh zadach, Izd-vo MGU, M., 1974

[3] Egorov A. I., Optimalnoe upravlenie teplovymi i diffuzionnymi protsessami, Nauka, M., 1978

[4] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972

[5] V. I. Krylov, Nachala teorii vychislitelnykh metodov. Uravneniya v chastnykh proizvodnykh, Nauka i tekhnika, Minsk, 1986

[6] Gabasov R., Kirillova F. M., Tyatyushkin A. I., Konstruktivnye metody optimizatsii, v. 1, Lineinye zadachi, Universitetskoe, Minsk, 1984

[7] Gabasov R., Kirillova F. M., Pavlenok N. S., “Optimalnoe upravlenie dinamicheskim ob'ektom po sovershennym izmereniyam ego sostoyanii”, Dokl. RAN, 444:4 (2012), 371–375

[8] Gabasov R., Kirillova F. M., Kuzmenkov D. S., “Optimalnoe upravlenie teplovym protsessom”, Dokl. NAN Belarusi, 53:1 (2009), 5–9