Two-person game with nash equilibrium in optimal control problems

被引：9
|
作者：
Antipin, Anatoly [1 ]
机构：
[1] Russian Acad Sci, Ctr Comp, Moscow 119333, Russia
来源：
OPTIMIZATION LETTERS | 2012年 / 6卷 / 07期
基金：
俄罗斯基础研究基金会;
关键词：
Two-person game; Nash equilibrium; Optimal control; Extra-gradient method;
D O I：
10.1007/s11590-011-0440-x
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
A two-person game with a Nash equilibrium is formulated for optimal control problems with a free right end and a linear differential system. The game is reduced to the calculation of a fixed point of an extremal mapping, which in turn is reduced to a variational inequality with linear constraints generated by systems of linear differential controllable processes. An extra-gradient iterative method is proposed for calculating the Nash equilibrium of the dynamic game. The convergence of the method is proved.
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页码：1349 / 1378
页数：30
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