Geodesic
On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set
Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 2, pp. 144-152

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 the players are described by the same ball with different time-dependent radii. The motion is constructed using polygonal lines. 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. The aim of the first player is to lead a phase vector to the terminal set at fixed time. The aim of the second player is the opposite. In this paper, a new approach to constructing of the first player control is proposed. Unlike the previously obtained results, the construction of such a control does not require the calculating of the outer radius of the maximal stable bridge at each time moment, which is an undoubted advantage of the proposed approach from the point of view of computational procedures creating.
Keywords: differential game, control, non-convex terminal set. 
@article{CHFMJ_2018_3_2_a1,
     author = {I. V. Izmestyev and V. I. Ukhobotov},
     title = {On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {144--152},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_2_a1/}
}
TY  - JOUR
AU  - I. V. Izmestyev
AU  - V. I. Ukhobotov
TI  - On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2018
SP  - 144
EP  - 152
VL  - 3
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_2_a1/
LA  - ru
ID  - CHFMJ_2018_3_2_a1
ER  - 
%0 Journal Article
%A I. V. Izmestyev
%A V. I. Ukhobotov
%T On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2018
%P 144-152
%V 3
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_2_a1/
%G ru
%F CHFMJ_2018_3_2_a1
I. V. Izmestyev; V. I. Ukhobotov. On an approach to constructing the control of the first player in a single-type differential game with a ring-shaped terminal set. Čelâbinskij fiziko-matematičeskij žurnal, Tome 3 (2018) no. 2, pp. 144-152. http://geodesic.mathdoc.fr/item/CHFMJ_2018_3_2_a1/