Existence of value and saddle point in infinite-dimensional differential games

被引：15

作者：

Ghosh, MK ^{[1
]}

Shaiju, AJ ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2004年 / 121卷 / 02期

基金：

美国国家科学基金会;

关键词：

differential games; existence of value; Hamilton-Jacobi-Isaacs equation; viscosity solutions; saddle-point equilibrium;

D O I：

10.1023/B:JOTA.0000037407.15482.72

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We study two-player zero-sum differential games of finite duration in a Hilbert space. Following the Berkovitz notion of strategies, we prove the existence of value and saddle-point equilibrium. We characterize the value as the unique viscosity solution of the associated Hamilton-Jacobi-Isaacs equation using dynamic programming inequalities.

引用

页码：301 / 325

页数：25

共 12 条

[1] CORRECTION AND ADDITION [J].

BERKOVITZ, LD .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1988, 26 (03) :740-742

[2] THE EXISTENCE OF VALUE AND SADDLE-POINT IN GAMES OF FIXED DURATION [J].

BERKOVITZ, LD .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1985, 23 (02) :172-196

[3]

BERKOVITZ LD, 1998, APPL MATH OPT, V17, P177

[4] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS IN INFINITE DIMENSIONS .4. HAMILTONIANS WITH UNBOUNDED LINEAR TERMS [J].

CRANDALL, MG ;

LIONS, PL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1990, 90 (02) :237-283

[5] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS IN INFINITE DIMENSIONS .5. UNBOUNDED LINEAR TERMS AND B-CONTINUOUS SOLUTIONS [J].

CRANDALL, MG ;

LIONS, PL .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 97 (02) :417-465

[6]

CRANDALL MG, 1994, LECT NOTES PURE APPL, V155, P51

[7]

Fattorini, 1999, INFINITE DIMENSIONAL, V62

[8] On differential games for infinite-dimensional systems with nonlinear, unbounded operators [J].

Kocan, M ;

Soravia, P ;

Swiech, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 211 (02) :395-423

[9]

KRASOVSKII NN, 1998, GAME THEORETICAL CON

[10]

Li X, 1995, Optimal Control Theory for Infinite-Dimensional Systems. Systems and Control: Foundations and Applications

← 1 2 →