MULTIGRID METHODS AND SPARSE-GRID COLLOCATION TECHNIQUES FOR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENTS

被引：47

作者：

Borzi, A. ^{[1
,2
,3
]}

von Winckel, G. ^{[2
]}

机构：

[1] Univ Sannio, Dipartimento Ingn, I-82100 Benevento, Italy

[2] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, A-8010 Graz, Austria

[3] Univ Sannio, Fac Ingn, I-82100 Benevento, Italy

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2009年 / 31卷 / 03期

基金：

奥地利科学基金会;

关键词：

multigrid method; sparse grids; reaction-diffusion problems; random fields; optimal control theory; PARTIAL-DIFFERENTIAL-EQUATIONS; RANDOM INPUT DATA; POLYNOMIAL INTERPOLATION; INVERSE PROBLEMS; DESIGN;

D O I：

10.1137/070711311

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An efficient computational framework to solve nonlinear parabolic optimal control problems with random coefficients is presented. This framework allows us to investigate the influence of randomness or uncertainty of problem's parameters values on the control provided by the optimal control theory. The proposed framework combines space-time multigrid methods with sparse-grid collocation techniques. Theoretical and numerical results of computation of stochastic optimal control solutions and formulation of mean control functions are presented.

引用

页码：2172 / 2192

页数：21

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