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.

引用

页码：1349 / 1378

页数：30

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