Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2018, Vol. 35 ›› Issue (5): 588-600.doi: 10.3969/j.issn.1005-3085.2018.05.010

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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).

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

CLC Number: