Geodesic
Construction of solutions in certain differential games with phase constraints
Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 513-539

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

A differential approach-evasion game with fixed termination time is studied. It is assumed that the phase vector of the conflict-control system is subjected to constraints that form a closed set in the position space. The ideology of stable bridges is used for solving the problem. A method of convolution is proposed, which is used in several problems for constructing explicitly the stable absorption operator defining the stable bridges. A method of approximate construction of the maximal stable bridge in this game is suggested. The relations are written down that define a system of sets approximating the maximal stable bridge, and a control procedure with a guide is described, which can be used for obtaining an approximate solution of the approach problem. 
@article{SM_2005_196_4_a2,
     author = {S. V. Grigor'eva and V. Yu. Pakhotinskikh and A. A. Uspenskii and V. N. Ushakov},
     title = {Construction of solutions in certain differential games with phase constraints},
     journal = {Sbornik. Mathematics},
     pages = {513--539},
     publisher = {mathdoc},
     volume = {196},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_4_a2/}
}
TY  - JOUR
AU  - S. V. Grigor'eva
AU  - V. Yu. Pakhotinskikh
AU  - A. A. Uspenskii
AU  - V. N. Ushakov
TI  - Construction of solutions in certain differential games with phase constraints
JO  - Sbornik. Mathematics
PY  - 2005
SP  - 513
EP  - 539
VL  - 196
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2005_196_4_a2/
LA  - en
ID  - SM_2005_196_4_a2
ER  - 
%0 Journal Article
%A S. V. Grigor'eva
%A V. Yu. Pakhotinskikh
%A A. A. Uspenskii
%A V. N. Ushakov
%T Construction of solutions in certain differential games with phase constraints
%J Sbornik. Mathematics
%D 2005
%P 513-539
%V 196
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2005_196_4_a2/
%G en
%F SM_2005_196_4_a2
S. V. Grigor'eva; V. Yu. Pakhotinskikh; A. A. Uspenskii; V. N. Ushakov. Construction of solutions in certain differential games with phase constraints. Sbornik. Mathematics, Tome 196 (2005) no. 4, pp. 513-539. http://geodesic.mathdoc.fr/item/SM_2005_196_4_a2/