OPTIMAL CONTROL OF THE PROPAGATION OF A GRAPH IN INHOMOGENEOUS MEDIA

被引：0

作者：

Deckelnick, Klaus ^{[1
]}

Elliott, Charles M. ^{[2
]}

Styles, Vanessa ^{[3
]}

机构：

[1] Univ Magdeburg, Inst Anal & Numer, D-39106 Magdeburg, Germany

[2] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

[3] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2009年 / 48卷 / 03期

关键词：

optimal control; eikonal equation; Hamilton-Jacobi equation; approximate controllability; HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS;

D O I：

10.1137/080723648

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 study an optimal control problem for viscosity solutions of a Hamilton-Jacobi equation describing the propagation of a one-dimensional graph with the control being the speed function. The existence of an optimal control is proved together with an approximate controllability result in the H(-1)-norm. We prove convergence of a discrete optimal control problem based on a monotone finite difference scheme and describe some numerical results.

引用

页码：1335 / 1352

页数：18

共 13 条

[1] Barles G., 1991, Asymptotic Analysis, V4, P271
[2] Berg J, 1996, IEEE DECIS CONTR P, P3376, DOI 10.1109/CDC.1996.573677
[3] Shape-based optimal estimation and design of curve evolution processes with application to plasma etching
Berg, JM
Zhou, N
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2001, 46 (12) : 1862 - 1873
[4] An alternating descent method for the optimal control of the inviscid burgers equation in the presence of shocks
Castro, Carlos
Palacios, Francisco
Zuazua, Enrique
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2008, 18 (03) : 369 - 416
[5] SOME PROPERTIES OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
CRANDALL, MG
EVANS, LC
LIONS, PL
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) : 487 - 502
[6] VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS
CRANDALL, MG
LIONS, PL
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 277 (01) : 1 - 42
[7] Deckelnick K, 2004, INTERFACE FREE BOUND, V6, P329
[8] Propagation of graphs in two-dimensional inhomogeneous media
Deckelnick, Klaus
Elliott, Charles M.
[J]. APPLIED NUMERICAL MATHEMATICS, 2006, 56 (09) : 1163 - 1178
[9] Ishii H., 1985, Bull. Fac. Sci. Engrg. Chuo Univ, V28, P33
[10] LADYZHENSKAYA OA, 1968, TRANSL MATH MONOGR, V24

← 1 2 →