Abstract
Consideration was given to the problem of optimal control of the mobile sources for systems obeying a parabolic equation together with systems of ordinary differential equations. The necessary conditions for optimality were established in the form of the pointwise and integral principles of maximum. The theoretical conclusions are illustrated by the solution of a numerical example
Similar content being viewed by others
References
Butkovskii, A.G. and Pustyl’nikov, L.M., Teoriya podvizhnogo upravleniya sistemami s raspredelennymi parametrami (Theory of Mobile Control of the Distributed-parameter Systems), Moscow: Nauka, 1980.
Kubyshkin, V.A. and Finyagina, V.I., Podvizhnoe upravlenie v sistemakh s raspredelennymi parametrami (Mobile Control in the Distributed-parameter Systems), Moscow: Sinteg, 2005.
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.
Ladyzhenskaya, O.A., Solonnikov, V.A., and Ural’tseva, N.N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa (Linear and Quasilinear Equations of Parabolic Type), Moscow: Nauka, 1976.
Ladyzhenskaya, O.A., Kraevye zadachi matematicheskoi fiziki (Boundary Problems of Mathematical Physics), Moscow: Nauka, 1973.
Tikhonov, A.N. and Arsenin, V.Ya., Metody resheniya nekorrektnykh zadach (Methods for Solution of Ill-posed Problems), Moscow: Nauka, 1974.
Vasil’ev, F.P., Metody resheniya ekstremal’nykh zadach (Methods for Solution of Extremal Problems), Moscow: Nauka, 1981.
Samarskii, A.A., Teoriya raznostnykh skhem (Theory of Difference Schemes), Moscow: Nauka, 1983.
Vasil’ev, F.P., Chislennye metody resheniya ekstremal’nykh zadach (Numerical Methods for Solution of Extremal Problems), Moscow: Nauka, 1988.
Mikhailov, V.P., Differentsial’nye uravneniya v chastnykh proizvodnykh (Partial Differential Equations), Moscow: Nauka, 1983.
Iosida, K., Funktsional’nyi analiz (Functional Analysis), Moscow: Mir, 1967.
Goebel, M., On Existence of Optimal Control, Math. Nachr., 1979, vol. 93, pp. 67–73.
Author information
Authors and Affiliations
Additional information
Original Russian Text © R.A. Teymurov, 2013, published in Avtomatika i Telemekhanika, 2013, No. 7, pp. 29–45.
Rights and permissions
About this article
Cite this article
Teymurov, R.A. On a problem of optimal control of mobile sources. Autom Remote Control 74, 1082–1096 (2013). https://doi.org/10.1134/S0005117913070035
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117913070035