Algorithms for computing Minkowski operators and their application in differential games

被引：14
|
作者：
Dvurechensky, P. E. [1 ]
Ivanov, G. E. [1 ]
机构：
[1] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2014年 / 54卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
Minkowski sum and difference; Minkowski operator; differential game; optimal control strategy; computational algorithms; errors of algorithms; OPTIMAL-CONTROL STRATEGY; CONSTRUCTION; PAYOFF;
D O I：
10.1134/S0965542514020055
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Minkowski operators are considered, which extend the concepts of the Minkowski sum and difference to the case where one of the summands depends on an element of the other term. The properties of these operators are examined. Convolution methods of computer geometry and algorithms for computing the values of the Minkowski operators are developed. These algorithms are used to construct epsilon-optimal control strategies in a nonlinear differential game with a nonconvex target set. The errors of the proposed algorithms are estimated in detail. Numerical results for the conflicting control of a nonlinear pendulum are presented.
引用
收藏
页码：235 / 264
页数：30
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