Geodesic
On a single-type differential game
Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 4, pp. 417-426.

Voir la notice de l'article provenant de la source Math-Net.Ru

In a normed space of finite dimension we consider a single-type differential game. The vectograms of players are described by the same ball with different time–depend radii. The motion is constructed using polygonal lines. A non-convex terminal payoff is specified, which is defined as the modulus of the deviation of the norm of the phase vector at a fixed point in time from a given value. The goal of the first player is to minimize this payoff. The goal of the second player is opposite. For this problem, the price of the game is found and the corresponding optimal controls of the players are constructed.
Keywords: control, differential game, payoff. 
@article{CHFMJ_2021_6_4_a2,
     author = {I. V. Izmestyev},
     title = {On a single-type differential game},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {417--426},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_4_a2/}
}
TY  - JOUR
AU  - I. V. Izmestyev
TI  - On a single-type differential game
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2021
SP  - 417
EP  - 426
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_4_a2/
LA  - ru
ID  - CHFMJ_2021_6_4_a2
ER  - 
%0 Journal Article
%A I. V. Izmestyev
%T On a single-type differential game
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2021
%P 417-426
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_4_a2/
%G ru
%F CHFMJ_2021_6_4_a2
I. V. Izmestyev. On a single-type differential game. Čelâbinskij fiziko-matematičeskij žurnal, Tome 6 (2021) no. 4, pp. 417-426. http://geodesic.mathdoc.fr/item/CHFMJ_2021_6_4_a2/

[1] Krasovskiy N.N., Subbotin A.I., Positional differential games, Nauka Publ., Moscow, 1974

[2] Isaacs R., Differential Games, John Wiley and Sons Publ., New York, 1965 | Zbl

[3] Pontryagin L.S., “Linear differential games of pursuit”, Mathematics of the USSR — Sbornik, 40:3 (1981), 285–303 | DOI | MR | Zbl | Zbl

[4] Ukhobotov V.I., “Synthesis of a control in single-type differential games with fixed time”, Bulletin of Chelyabinsk University. Mathematics. Mechanics, 1996, no. 3, 178–184 (In Russ.) | MR

[5] Izmest'ev I. V., Ukhobotov V. I., “On a one-dimensional differential game with a non-convex terminal payoff”, Lecture Notes in Computer Science, 12095 (2020), 200–211 | DOI

[6] Kolmogorov A.N., Fomin S.V., Elements of the theory of functions and functional analysis, Nauka Publ., Moscow, 1972 (In Russ.)

[7] Izmest'ev I.V., Ukhobotov V.I., “On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set”, Chelyabinsk Physical and Mathematical Journal, 3:2 (2018), 144–152 (In Russ.) | MR

[8] Ukhobotov V.I., Method of one-dimensional design in linear differential games with integral constraints, Chelyabinsk State University, Chelyabinsk, 2005 (In Russ.)