基于楔形基函数的微分博弈两点边值问题的逼近

J4 ›› 2011, Vol. 46 ›› Issue (8): 38-41.

基于楔形基函数的微分博弈两点边值问题的逼近

田双亮¹,房保言¹*, 王志刚²

1.西北民族大学数学与计算机科学学院, 甘肃兰州 730030;
2.西安交通大学阳光中学, 陕西西安 710043

出版日期:2011-08-20 发布日期:2011-09-08
通讯作者: 房保言(1984- ),女,硕士研究生,研究方向为博弈论与组合优化. Email:fangbaoyan0820@126.com
作者简介:田双亮(1965- ),男,教授,主要从事应用数学的研究. Email: sl-tian@163.com
基金资助:
国家民委科研基金资助项目(10xb01);西北民族大学研究生科研创新基金资助项目(ycx10114)

Approximation method for two-point boundary value problem of differential game based on ridge basis function

TIAN Shuang-liang¹, FANG Bao-yan¹*, WANG Zhi-gang²

1. School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, China;
2. Sunshine Middle School Attached to Xi′an Jiaotong University, Xi′an 710043, Shaanxi, China

Online:2011-08-20 Published:2011-09-08

摘要/Abstract

摘要：

微分博弈的研究已经有了一系列的结果,但是如何构造更有效的数值算法求解鞍点策略的近似解,仍是一个开放问题。基于楔形基函数,构造了一种新的求解微分博弈两点边值问题的数值方法,给出了解的存在惟一性,并通过算例验证了算法的可行性,为鞍点策略的近似解的求解提供了一种有效的方法。

关键词: 微分博弈;两点边值问题;楔形基函数

Abstract:

The study of differential game has yielded a number of substantial results. However, numerical method for saddle point strategy is still open question. In this paper, a new method with ridge basis function for twopoint boundary value problem of differential game is developed, where the existence and uniqueness of the solution of twopoint boundary value problem is established and discussed.Also, the method is applied to numerical examples to examine its appropriateness. It will be a useful way to solving the numerical solutions of saddle point strategy.

Key words: differential game; two-point boundary value problem; ridge basis function

田双亮1,房保言1*, 王志刚2. 基于楔形基函数的微分博弈两点边值问题的逼近[J]. J4, 2011, 46(8): 38-41.

TIAN Shuang-liang1, FANG Bao-yan1*, WANG Zhi-gang2. Approximation method for two-point boundary value problem of differential game based on ridge basis function[J]. J4, 2011, 46(8): 38-41.

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