Geodesic
On calculating the value of a differential game in the class of counterstrategies
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 59-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a linear dynamic system with control and disturbance, a feedback control problem is considered, in which the Euclidean norm of the set of deviations of the system's motion from given targets at given times is optimized. The problem is formalized into a differential game in “strategy-counterstrategy” classes. A game value computing procedure, which reduces the problem to a recursive construction of upper convex hulls of auxiliary functions, is justified. Results of numerical simulations are presented.
Keywords: differential games, value of the game, saddle point, counterstrategies. 
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M. I. Gomoyunov; D. V. Kornev. On calculating the value of a differential game in the class of counterstrategies. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 1, pp. 59-68. http://geodesic.mathdoc.fr/item/TIMM_2013_19_1_a5/

[1] Krasovskii N. N., Upravlenie dinamicheskoi sistemoi, Nauka, M., 1985, 516 pp. | MR

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

[3] Krasovskii N. N., “K zadache unifikatsii differentsialnykh igr”, Doklady AN SSSR, 226:6 (1976), 1260–1263 | MR

[4] Krasovskii A. N., “Postroenie smeshannykh strategii na osnove stokhasticheskikh programm”, Prikl. matematika i mekhanika, 51:2 (1987), 186–192 | MR

[5] Krasovskii A. N., Krasovskii N. N., Control under lack of information, Birkhäuser, Berlin etc., 1995, 322 pp. | MR

[6] Subbotin A. I., Minimaksnye neravenstva i uravneniya Gamiltona–Yakobi, Nauka, M., 1991, 216 pp. | MR | Zbl

[7] Lukoyanov N. Yu., “Odna differentsialnaya igra s neterminalnoi platoi”, Izv. RAN. Teoriya i sistemy upravleniya, 1997, no. 1, 85–90 | Zbl

[8] Lukoyanov N. Yu., “K voprosu vychisleniya tseny differentsialnoi igry dlya pozitsionnogo funktsionala”, Prikl. matematika i mekhanika, 62:2 (1998), 188–198 | MR | Zbl

[9] Blagodatskikh V. I., Filippov A. F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Tr. MIAN SSSR, 169, 1985, 194–252 | MR | Zbl

[10] Krasovskii A. N., Reshetova T. N., Upravlenie pri defitsite informatsii, Ucheb. posobie, UrGU, Sverdlovsk, 1990, 104 pp.

[11] Kornev D. V., “O chislennom reshenii pozitsionnykh differentsialnykh igr s neterminalnoi platoi”, Avtomatika i telemekhanika, 2012, no. 11, 60–75