Construction of a Maximal Stable Bridge in Games with Simple Motions on the Plane

被引：3

作者：

Kamneva, L. V. ^{[1
,2
]}

Patsko, V. S. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Ural Branch, Inst Math & Mech, Ul S Kovalevskoi 16, Ekaterinburg 620990, Russia

[2] Ural Fed Univ, Ul Mira 19, Ekaterinburg 620002, Russia

来源：

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2016年 / 292卷

基金：

俄罗斯基础研究基金会;

关键词：

differential games with simple motions on the plane; solvability set; backward procedure;

D O I：

10.1134/S0081543816020115

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is known that the solvability set (the maximal stable bridge) in a zero-sum differential game with simple motions, fixed terminal time, geometric constraints on the controls of the first and second players, and convex terminal set can be constructed by means of a program absorption operator. In this case, a backward procedure for the construction of t-sections of the solvability set does not need any additional partition times. We establish the same property for a game with simple motions, polygonal terminal set (which is generally nonconvex), and polygonal constraints on the players' controls on the plane. In the particular case of a convex terminal set, the operator used in the paper coincides with the program absorption operator.

引用

页码：S125 / S139

页数：15