Construction of a maximal stable bridge in games with simple motions on the plane

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 t...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics 2016-04, Vol.292 (Suppl 1), p.125-139
Main Authors: Kamneva, L. V., Patsko, V. S.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0081-5438
1531-8605
DOI:10.1134/S0081543816020115