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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (5): 588-600.doi: 10.3969/j.issn.1005-3085.2018.05.010

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两目标两局中人的混杂微分博弈系统识别域的判别（英）

韩艳丽1,   高   岩2   

  1. 1- 河南理工大学数学与信息科学学院，焦作  454000
    2- 上海理工大学管理学院，上海  200093
  • 收稿日期:2016-01-15 接受日期:2018-06-07 出版日期:2018-10-15 发布日期:2018-12-15
  • 基金资助:
    国家自然科学基金(11171221)；高等教育博士点研究基金(20123120110004)；河南省高等学校重点研究项目计划(17A120010).

Determining the Discriminating Domain for Hybrid Differential Game with Two Targets and Two Players

HAN Yan-li1,   GAO Yan2   

  1. 1- School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000
    2- School of Management, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2016-01-15 Accepted:2018-06-07 Online:2018-10-15 Published:2018-12-15
  • Supported by:
    The National Natural Science Foundation of China (11171221); the Research Fund for the Doctoral Program of Higher Education of China (20123120110004); the Key Research Project Plan of Institutions of Higher of Henan Province (17A120010).

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摘要： 混杂微分博弈系统融合了控制工程、数学和计算机等多门学科，其研究无论在理论上还是实际应用中都有很高的价值．本文讨论了两目标两局中人的混杂微分博弈系统的识别域判别问题．首先，利用非光滑分析，讨论两目标两局中人的连续微分博弈系统在分片光滑函数构成的区域上识别域的判别问题，我们得到判别识别域问题可以转化成求解不等式组的解的存在问题．最后，将此结论推广到两目标两局中人的混杂微分博弈系统．本文的创新之处在于，我们解决的是包含两个控制变量的微分博弈识别域的判别问题，而不是包含一个控制变量的微分包含问题．

关键词: 混杂微分博弈, 识别域, 分片光滑函数

Abstract: Hybrid differential game combines the control engineering, mathematics and computer science. The research has a high value no matter in theory or in practical applications. In this paper, the discriminating domain of hybrid differential game with two targets and two players is discussed based on this theory. Firstly, the discriminating domain of continuous differential game on a region where the functions are piecewise smooth is discussed using nonsmooth analysis. Then, we find that the problem of determining the discriminating domain can be transformed into determining the solution of the inequalities. Finally, the result is generalized to the hybrid differential game. The novelty is that we propose the method of discriminating domain for differential game which contains two control variables, not one control variable as in differential inclusion.

Key words: hybrid differential game, discriminating domain, piecewise smooth function

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