On Some Control Problems
Informatics and Automation, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 208-217.

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This article deals with some aspects of typical control problems for dynamical systems, whose evolution is described by differential equations, first by ordinary differential equations and then by equations with time lag. Open and closed loop problems are considered. We are mostly interested in closed loop problems under lack of information on dynamical and informational disturbances. We discuss such notions as an adequate informational image, which determines the character of a strategy; types of strategies: pure and mixed strategies; procedures for the observation and estimation of the current phase state on the basis of the available informational image.
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N. N. Krasovskii. On Some Control Problems. Informatics and Automation, Algebra. Topology. Differential equations and their applications, Tome 224 (1999), pp. 208-217. http://geodesic.mathdoc.fr/item/TRSPY_1999_224_a12/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961, 391 pp. | MR

[2] Bellman R., Dinamicheskoe programmirovanie, Izd-vo inostr. lit., M., 1960, 400 pp. | MR

[3] Kalman R. E., “Ob obschei teorii sistem upravleniya”, Tr. I Mezhdunar. kongr. po avtomaticheskomu upravleniyu, Izd-vo AN SSSR, M., 1960, 29 | MR

[4] Krasovskii N. N., Teoriya upravleniya dvizheniem, Nauka, M., 1968, 475 pp. | MR

[5] Osipov Yu. S., “K teorii differentsialnykh igr sistem s posledeistviem”, PMM, 35:2 (1971), 300–311 | MR | Zbl

[6] Kurzhanskii A. B., Upravlenie i nablyudenie v usloviyakh neopredelennosti, Nauka, M., 1977, 392 pp. | MR | Zbl

[7] Krasovskii A. N., Krasovskii N. N., Control under lack of information, Birkhäuser, Boston, 1995, 320 pp. | MR

[8] Aizeks R., Differentsialnye igry, Mir, M., 1967, 479 pp. | MR

[9] Liptser R. Sh., Shiryaev A. N., Statistika sluchainykh protsessov, Nauka, M., 1974, 696 pp. | MR | Zbl

[10] Krasovskii N. N., Subbotin A. I., Pozitsionnye differentsialnye igry, Nauka, M., 1974, 456 pp. | MR | Zbl

[11] Subbotin A. I., Minimaksnye neravenstva i uravneniya Gamiltona–Yakobi, Nauka, M., 1991, 215 pp. | MR

[12] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 518 pp. | MR