线性微分博弈系统的识别域判别-控制与决策.pdf

第30 卷 第7 期 控 制 与 决 策 2015 年 7 月 Vol. 30 No. 7 Control and Decision Jul. 2015 文章编号: 1001-0920 (2015) 07-1329-04 DOI: 10.13195/j.kzyjc.2014.0876 线性微分博弈系统的识别域判别 1,2 1 韩艳丽 , 高 岩 (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) 摘 要: 针对一般非线性系统识别域的判别定理难以被具体应用这一现象, 利用非光滑分析理论, 研究线性微分博 弈系统的一个有界识别域问题, 即如果一个闭集是识别域, 则此集合的凸包也是识别域, 从而得到一个多面体识别 域. 提出了该问题的一种有效算法, 该算法简便易行, 利用转换定理即可得到系统的胜利域. 最后通过算例验证了所 提出算法的可行性和有效性. 关键词: 博弈论；微分博弈；识别域；非光滑分析 中图分类号: O231.2 文献标志码: A Determining discriminating domain for linear differential games HAN Yan-li1,2 , GAO Yan1 (1. Business School，University of Shanghai for Science and Technology ，Shanghai 200093，China ；2. School of Mathematics and Information Science ，He’nan Polytechnic University ，Jiaozuo 454003 ，China ．Correspondent ：HAN Yan-li ，E-mail ：hanyl@hpu.edu.cn) Abstract: Aimming at the phenomenon that the discriminating theorem of discriminating domain of the general nonlinear system is difficult to be used, a bounded discriminating domain for linear pursuit-evasion differential games is studied. If a closed set is a discriminating domain of the differential games, the convex hull of the set is also a discriminating domain of the differential games. A polyhedral discriminating domain is obtained, and an efficient algorithm is given, which is easy to be used. By using the alternative theorem, the victory domain of the differential games can be obtained. An example is given to show the feasibility and effectiveness of the proposed algorithm. Keywords: game theory ；differential games ；discriminating domain ；nonsmooth analysis 0 引引引 言言言