Semicontinuous solutions of Hamilton-Jacobi-Bellman equations with degenerate state constraints

被引：36

作者：

Frankowska, H ^{[1
]}

Plaskacz, S

机构：

[1] Univ Paris 09, CNRS, ERS2064, F-75775 Paris 16, France

[2] Nicholas Copernicus Univ, Dept Math & Informat, PL-87100 Torun, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2000年 / 251卷 / 02期

关键词：

viability theory; lower semicontinuous solutions; Hamilton-Jacobi-Bellman equations; optimal control under state constraints;

D O I：

10.1006/jmaa.2000.7070

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the value function of a Bolza optimal control problem with state constraints is characterized as the unique lower semicontinuous solution of a Hamilton-Jacobi equation. The state constraints are given by an arbitrary closed set with possibly empty interior. In particular, Soner's inward pointing condition is extended here to the case of degenerate state constraints. (C) 2000 Academic Press.

引用

页码：818 / 838

页数：21

共 17 条

[1]

[Anonymous], 1947, ANN U GRENOBLE

[2]

Aubin J. P., 1990, Set-valued analysis, DOI 10.1007/978-0-8176-4848-0

[3]

Aubin JP., 1991, Viability Theory

[4]

BARRON EN, 1990, COMMUN PART DIFF EQ, V15, P1713

[5]

Bouligand G., 1932, Introduction a la Geometrie Infinitesimale Directe

[6] HAMILTON-JACOBI EQUATIONS WITH STATE CONSTRAINTS [J].

CAPUZZODOLCETTA, I ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 318 (02) :643-683

[7] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS [J].

CRANDALL, MG ;

LIONS, PL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) :1-42

[8] Filippov's and Filippov-Wazewski's theorems on closed domains [J].

Frankowska, H ;

Rampazzo, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) :449-478

[9] Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems [J].

H. Frankowska ;

R. B. Vinter .

Journal of Optimization Theory and Applications, 2000, 104 (1) :20-40

[10] OPTIMAL TRAJECTORIES ASSOCIATED WITH A SOLUTION OF THE CONTINGENT HAMILTON-JACOBI EQUATION [J].

FRANKOWSKA, H .

APPLIED MATHEMATICS AND OPTIMIZATION, 1989, 19 (03) :291-311

← 1 2 →