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
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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/