Geodesic
On some problems in geometric games theory
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 131-137 
L. Yu. Blazhennova-Mikulich. On some problems in geometric games theory. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 8, pp. 131-137. http://geodesic.mathdoc.fr/item/FPM_2005_11_8_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Several problems of dynamic systems control can be reduced to geometric games. The problem of stabilization is an example. In this paper the criteria of a saddle point in a geometric game is proved under more general conditions than earlier. Algorithms for finding of a saddle point are given in cases where the strategy set of one of the players is (1) a ball in $\mathbb R^n$, (2) a closed interval, (3) a polyhedral, and the strategy set of the other player is an arbitrary convex set.

[1] Aleksandrov V. V., Blazhennova-Mikulich L. Yu., Gutieres-Arias I. M., Lemak S. S., “Myagkoe testirovanie tochnosti stabilizatsii i sedlovye tochki v geometricheskikh igrakh”, Vestn. Mosk. un-ta. Ser. 1, Matematika, mekhanika, 2005, no. 1, 43–50 | MR | Zbl

[2] Petrosyan L. A., Zenkevich N. A., Semina E. A., Teoriya igr, Vysshaya shkola, Knizhnyi dom “ Universitet”, M., 1998, 66–68 | MR