Minimax risk (regret) strategy for one class of control problems under dynamic disturbances
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 192-200
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A controlled system under dynamic disturbances is considered. We formulate the problem of finding a strategy that is optimal in the sense of Savage's minimax risk (regret) criterion, list basic properties of such problems, and describe a construction of a strategy optimal in the above sense for one class of systems containing linear systems.
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D. A. Serkov. Minimax risk (regret) strategy for one class of control problems under dynamic disturbances. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 192-200. http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a17/

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

[2] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985 | MR

[3] Subbotin A. I., Chentsov A. G., Optimizatsiya garantii v zadachakh upravleniya, Nauka, M., 1981 | MR

[4] Subbotin A. I., Obobschennye resheniya uravnenii v chastnykh proizvodnykh pervogo poryadka. Perspektivy dinamicheskoi optimizatsii, In-t kompyuternykh issledovanii, M.–Izhevsk, 2003

[5] Serkov D. A., “Silno optimalnye strategii”, Dokl. AN SSSR, 321:2 (1991), 258–262 | MR | Zbl

[6] Serkov D. A., “O ravnomernykh strategiyakh”, Sb. tr. mezhdunar. seminara “Teoriya upravleniya i teoriya obobschennykh reshenii uravnenii Gamiltona–Yakobi” (CGS'2005), posvyaschennogo 60-letiyu akademika A. I. Subbotina, T. 1, Izd-vo Ural. un-ta, Ekaterinburg, 2006, 273–284

[7] Serkov D. A., “Strategii minimaksnogo riska (sozhaleniya) v sisteme s prostymi dvizheniyami”, Tr. In-ta matematiki i mekhaniki UrO RAN, 13, no. 3, 2007, 121–135

[8] Savage L. J., “The theory of statistical decision”, J. Amer. Stat. Association, 46 (1951), 55–67 | DOI | Zbl

[9] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR