Geodesic
On a discrete game problem with non-convex control vectograms
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 48-58.

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

In a normed space of finite dimension, a discrete game problem with fixed duration is considered. The terminal set is determined by the condition that the norm of the phase vector belongs to a segment with positive ends. In this paper, a set defined by this condition is called a ring. At each moment, the vectogram of the first player's controls is a certain ring. The controls of the second player at each moment are taken from balls with given radii. The goal of the first player is to lead a phase vector to the terminal set at a fixed time. The goal of the second player is the opposite. In this paper, necessary and sufficient termination conditions are found, and optimal controls of the players are constructed.
Keywords: game, control, vectogram, terminal set. 
@article{IIMI_2021_58_a2,
     author = {I. V. Izmestyev and V. I. Ukhobotov},
     title = {On a discrete game problem with non-convex control vectograms},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {48--58},
     publisher = {mathdoc},
     volume = {58},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/}
}
TY  - JOUR
AU  - I. V. Izmestyev
AU  - V. I. Ukhobotov
TI  - On a discrete game problem with non-convex control vectograms
JO  - Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
PY  - 2021
SP  - 48
EP  - 58
VL  - 58
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/
LA  - ru
ID  - IIMI_2021_58_a2
ER  - 
%0 Journal Article
%A I. V. Izmestyev
%A V. I. Ukhobotov
%T On a discrete game problem with non-convex control vectograms
%J Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
%D 2021
%P 48-58
%V 58
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/
%G ru
%F IIMI_2021_58_a2
I. V. Izmestyev; V. I. Ukhobotov. On a discrete game problem with non-convex control vectograms. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 58 (2021), pp. 48-58. http://geodesic.mathdoc.fr/item/IIMI_2021_58_a2/

[1] Isaacs R., Differential games, John Wiley and Sons, New York, 1965 | Zbl

[2] Shorikov A. F., “An algorithm of adaptive minimax control for the pursuit–evasion process in discrete-time dynamical system”, Proceedings of the Steklov Institute of Mathematics, 2000, suppl. 2, 173–190 | Zbl

[3] Raxmanov A., Ibragimov G., “Linear discrete pursuit game with phase constraints”, The Scientific World Journal, 2014 (2014), 435103, 5 pp. | DOI

[4] Bopardikar S. D., Suri S., “$k$-Capture in multiagent pursuit evasion, or the lion and the hyenas”, Theoretical Computer Science, 522 (2014), 13–23 | DOI | Zbl

[5] Sokolov V. F., “Problems of adaptive optimal control of discrete-time systems under bounded disturbance and linear performance indexes”, Automation and Remote Control, 79:6 (2018), 1086–1099 | DOI | Zbl

[6] Ukhobotov V. I., Stabulit I. S., “Dynamic control problem under interference with a given set of correction momenta”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 28:1 (2018), 74–81 (in Russian) | DOI | Zbl

[7] Casini M., Criscuoli M., Garulli A., “A discrete-time pursuit–evasion game in convex polygonal environments”, Systems and Control Letters, 125 (2019), 22–28 | DOI | Zbl

[8] Nikitina S. A., Ukhobotov V. I., “Discrete dynamic control problem with terminal set in form of ring”, Vestnik Rossiiskoi Akademii Estestvennykh Nauk, 19:2 (2019), 120–121 (in Russian)

[9] Izmest'ev I. V., “Discrete game problem with ring-shaped terminal set”, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 30:1 (2020), 18–30 (in Russian) | DOI

[10] Pshenichnyi B. N., Sagaidak M. I., “Differential games of prescribed duration”, Cybernetics, 6:2 (1970), 72–83 | DOI | Zbl

[11] Pontryagin L. S., “Linear differential games. II”, Soviet Mathematics. Doklady, 8 (1967), 910–912 | Zbl

[12] Ukhobotov V. I., “Single-type differential game with terminal set in form of a ring”, Some problems of dynamic and control, Transactions, Chelyabinsk State University, Chelyabinsk, 2005, 108–123 (in Russian)