DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS

doi:10.1016/S0252-9602(17)30093-0

Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (6): 1594-1606.doi: 10.1016/S0252-9602(17)30093-0

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DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS

Yanli HAN, Yan GAO

School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received:2017-01-05 Revised:2017-03-01 Online:2017-12-25 Published:2017-12-25
Contact: Yan GAO E-mail:gaoyan@usst.edu.cn
Supported by:
This work was supported by National Science Foundation of China (11171221), Doctoral Program Foundation of Institutions of Higher Education of China (20123120110004), Natural Science Foundation of Shanghai (14ZR1429200), Innovation Program of Shanghai Municipal Education Commission (15ZZ073) and Key Research Project Plan of Institutions of Higher of Henan Province (17A120010).

Abstract

Abstract:

This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron.

Key words: viability, hybrid linear differential game, discriminating domain, nonsmooth analysis

Yanli HAN, Yan GAO. DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS[J].Acta mathematica scientia,Series B, 2017, 37(6): 1594-1606.

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DETERMINING THE DISCRIMINATING DOMAIN FOR HYBRID LINEAR DIFFERENTIAL GAME WITH TWO PLAYERS AND TWO TARGETS

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