Geodesic
Necessary and sufficient optimality conditions and uniqueness conditions for optimizing functions for control systems of general type
Izvestiya. Mathematics, Tome 6 (1972) no. 3, pp. 649-676 
V. I. Plotnikov. Necessary and sufficient optimality conditions and uniqueness conditions for optimizing functions for control systems of general type. Izvestiya. Mathematics, Tome 6 (1972) no. 3, pp. 649-676. http://geodesic.mathdoc.fr/item/IM2_1972_6_3_a11/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this work we establish necessary and sufficient optimality conditions, and a theorem on the uniqueness of optimizing functions for control systems of general type.

[1] Sirazetdinov T. K., “K teorii optimalnykh protsessov s raspredelennymi parametrami”, Avtomatika i telemekhanika, XXV:4 (1964), 463–472 | MR

[2] Egorov A. I., “Ob optimalnom upravlenii protsessami v raspredelennykh ob'ektakh”, Prikl. matem. i mekhan., XXVII:4 (1963), 688–696

[3] Egorov A. I., “Optimalnye protsessy v sistemakh s raspredelennymi parametrami i nekotorye zadachi teorii invariantnosti”, Izv. AN SSSR. Ser. matem., 29 (1965), 1205–1260 | MR | Zbl

[4] Egorov A. I., “Neobkhodimye usloviya optimalnosti dlya sistem s raspredelennymi parametrami”, Matem. sb., 69(111) (1966), 371–421 | MR | Zbl

[5] Egorov Yu. V., “Neobkhodimye usloviya optimalnosti upravleniya v banakhovom prostranstve”, Matem. sb., 64(106) (1964), 79–101 | MR | Zbl

[6] Egorov Yu. V., “Nekotorye zadachi optimalnogo upravleniya”, Zh. vychisl. matem. i matem. fiz., 3:5 (1963), 887–904

[7] Butkovskii A. G., Teoriya optimalnogo upravleniya sistemami s raspredelennymi parametrami, Nauka, M., 1965 | MR | Zbl

[8] Lions J. L., “Sur le contrôle optimal de systémes, décrits par des équations aux dérivees partielles linéaires. Remarques générates”, Compt. Rend. Acad. Sci., 263 (1966), A661–A663 | MR

[9] Lions J. L., “Sur le contrôle optimal de systémes, décrits par des équations aux dérivees partielles liinéaires. Equations elliptiques”, Compt. Rend. Acad. Sci., 20 (1966), A713–A715 | MR

[10] Lions J. L., “Sur le contrôle optimal de systémes décrits par des équations aux dérivees partielles linéaires. Equations devolution”, Compt. Rend. Acad. Sci., 21 (1966), A776–A779

[11] Lions J. L., “Control problems in systemes described by partial differential equations.”, Math. Theory of Control, Acad. Press., New York, London, 1967, 251–271 | MR

[12] Plotnikov V. I., “Teoremy suschestvovaniya optimiziruyuschikh funktsii”, Izv. AN SSSR. Ser. matem., 34 (1970), 689–711 | MR | Zbl

[13] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, Gos. izd-vo fiz.-matem. lit-ry, M., 1959 | MR

[14] Danford N., Shvarts Dzh. T., Lineinye operatory, IL, M., 1962

[15] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Gos. izd-vo fiz.-matem. lit-ry, M., 1961

[16] Boltyanskii V. G., Matematicheskie metody optimalnogo upravleniya, Nauka, M., 1969 | MR

[17] Plotnikov V. I., “Energeticheskoe neravenstvo i svoistvo pereopredelennosti sistemy sobstvennykh funktsii”, Izv. AN SSSR. Ser. matem., 32 (1968), 743–755 | MR | Zbl