Invariant solutions of differential games and Hamilton-Jacobi-Isaacs equations for time-measurable Hamiltonians

被引：25
作者：
Cardaliaguet, P
Plaskacz, S
机构：
[1] Univ Paris 09, Ctr VJC, ERS 2064, F-75775 Paris, France
[2] Nicholas Copernicus Univ, Dept Math & Informat, PL-87100 Torun, Poland
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2000年 / 38卷 / 05期
关键词：
differential games; Hamilton-Jacobi-Isaacs equation; viscosity solutions; time-measurable Hamiltonians;
D O I：
10.1137/S0363012998296219
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We characterize invariance of time-varying domains with respect to differential games with time-measurable dynamics. We deduce from this result a new definition of viscosity solutions to some first order Hamilton-Jacobi equations with time-measurable Hamiltonians.
引用
收藏
页码：1501 / 1520
页数：20
相关论文
共 18 条
[1]  
[Anonymous], 1985, B FACUL SCI ENG CHUO
[2]  
Aubin J. P., 1990, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0
[3]  
Aubin J.-P., 1984, DIFFERENTIAL INCLUSI
[4]  
Aubin JP., 1991, Viability Theory
[5]   DISCONTINUOUS VISCOSITY SOLUTIONS OF 1ST-ORDER HAMILTON-JACOBI EQUATIONS - A GUIDED VISIT [J].
BARLES, G .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1993, 20 (09) :1123-1134
[6]   OPTIMAL-CONTROL AND SEMICONTINUOUS VISCOSITY SOLUTIONS [J].
BARRON, EN ;
JENSEN, R .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 113 (02) :397-402
[7]   GENERALIZED VISCOSITY SOLUTIONS FOR HAMILTON-JACOBI EQUATIONS WITH TIME-MEASURABLE HAMILTONIANS [J].
BARRON, EN ;
JENSEN, R .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1987, 68 (01) :10-21
[8]   A differential game with two players and one target [J].
Cardaliaguet, P .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1996, 34 (04) :1441-1460
[9]  
CARDALIAGUET P, 1996, BANACH CTR PUBL, V35, P149
[10]   VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].
CRANDALL, MG ;
LIONS, PL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42
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