Geodesic
The program iterations method in game problem of guidance and set-valued quasistrategies
Ural mathematical journal, Tome 2 (2016) no. 1, pp. 17-37 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a differential game of guidance-evasion, which is solved with the program iterations method. The iterated procedure is realized in the space of sets, the elements of which are the game's positions. The objective of this procedure is to construct the alternative partition of the space of positions as established by N.N. Krasovskii and A.I. Subbotin. In addition, more general assumptions on topological properties of the set defining the phase constraints are considered. The connection with the game's solution in the class of quasistrategies is investigated. These quasistrategies are defined as set-valued mappings on spaces of strategic (countably additive) Borel measures.
Keywords: Differential game, Iterated procedure, Quasistrategy. 
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Alexander G. Chentsov. The program iterations method in game problem of guidance and set-valued quasistrategies. Ural mathematical journal, Tome 2 (2016) no. 1, pp. 17-37. http://geodesic.mathdoc.fr/item/UMJ_2016_2_1_a2/

[1] Isaacs R., Differential game, John Wiley, New York, 1965, 384 pp.

[2] Krasovskii N.N. and Subbotin A.I., Game-theoretical control problems, Springer–Verlag, New York–Berlin–Heidelberg, 1988

[3] Krasovskii N.N. and Subbotin A.I., “An Alternative for the Game Problem of Convergence”, J. Appl. Math. Mech, 34:6 (1971), 948–965

[4] Chentsov A.G., “On the structure of a game problem of convergence”, Soviet Math. Dokl, 16 (1975), 1404–1406 (in Russian)

[5] Chentsov A.G., “On a game problem of guidance”, Soviet Mathematics, 17:1 (1976), 73–77 (in Russian)

[6] Chentsov A.G., “On a game problem of converging at a given instant of time”, Mathematics of the USSR-Sbornik, 28:3 (1976), 353–376 (in Russian)

[7] Chistiakov S.V., “On solving pursuit game problems”, J. of Applied Mathematics and Mechanics, 41:5 (1977), 855–852 | DOI

[8] Ukhobotov V.I., “Construction of a stable bridge for a class of linear games”, J. of Applied Mathematics and Mechanics, 41:2 (1977), 350–354 | DOI