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基于生存理论的线性微分博弈系统识别域的判别

韩艳丽1,2,*  高岩1   

  1. 1. 上海理工大学管理学院, 上海 200093; 2. 河南理工大学数信学院, 河南焦作 454003;
  • 收稿日期:2015-04-02 出版日期:2016-03-15 发布日期:2016-03-15
  • 通讯作者: 韩艳丽 hanyl@hpu.edu.cn
  • 基金资助:

    国家自然科学基金(No. 11171221), 教育部博士点基金(No. 20123120110004), 上海市一流学科(No. XTKX2012), 上海市自然科学基金(No. 14ZR1429200), 河南省软科学研究计划项目(No. 162400410274)

Determining the discriminating domain for linear differential games based on viability theory

HAN Yanli1,2,*  GAO Yan1   

  1. 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China; 2.  School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, Henan, China
  • Received:2015-04-02 Online:2016-03-15 Published:2016-03-15

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摘要：

利用生存性理论, 研究线性微分博弈系统的一个有界识别域问题. 采用生存性理论来研究线性微分博弈系统的有界多面体\,(有限点集的凸包)\,的识别域问题, 给定的方法只需要检验该多面体在极点处是否满足生存性条件. 进而, 利用生存性与识别域的关系, 即可判断此多面体是否是系统的识别域, 简便易行.

关键词: 微分博弈, 生存性理论, 识别域, 非光滑分析

Abstract:

This paper studies a bounded discriminating domain for linear pursuit-evasion differential games using viability theory. Researching a bounded polyhedron who is a convex hull of finite points for the discriminating domain of linear differential games by viability theory, we just need to test whether the extreme points of the polyhedron meet the viability conditions. Then, using the relationship between viability and discriminating domain, we can determine whether the polyhedron is the discriminating domain of the differential games. It is easy to be used.

Key words: differential games, viability theory, discriminating domain, nonsmooth analysis