Error estimates for the regularization of optimal control problems with pointwise control and state constraints

被引：0

作者：

Cherednichenko, S. ^{[1
]}

Roesch, A. ^{[1
]}

机构：

[1] Univ Duisburg Essen, Fachbereich Math, D-47057 Duisburg, Germany

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2008年 / 27卷 / 02期

关键词：

optimal control; linear-quadratic problems; state constraints; Lavrentiev regularization; perturbations; stability;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss a linear-quadratic optimal control problem with pointwise control and state constraints. The state constraints are regularized by a Lavrentiev type regularization. The main results of the paper are estimates for the regularization error and the stability with respect to noisy data.

引用

页码：195 / 212

页数：18

共 10 条

[1] ON THE APPROXIMATION OF INFINITE OPTIMIZATION PROBLEMS WITH AN APPLICATION TO OPTIMAL-CONTROL PROBLEMS [J].

ALT, W .

APPLIED MATHEMATICS AND OPTIMIZATION, 1984, 12 (01) :15-27

[2] BOUNDARY CONTROL OF SEMILINEAR ELLIPTIC-EQUATIONS WITH POINTWISE STATE CONSTRAINTS [J].

CASAS, E .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1993, 31 (04) :993-1006

[3] Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution equation [J].

Janno, J .

INVERSE PROBLEMS, 2000, 16 (02) :333-348

[4]

Lavrentiev M.M., 1967, SOME IMPROPERLY POSE

[5]

LIU FS, 1996, LECT NOTES PURE APPL, V177, P353

[6] Optimal control of PDEs with regularized pointwise state constraints [J].

Meyer, C ;

Rösch, A ;

Tröltzsch, F .

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 2006, 33 (2-3) :209-228

[7]

Nair MT, 2004, Z ANAL ANWEND, V23, P167

[8] Existence of regular Lagrange multipliers for a nonlinear elliptic optimal control problem with pointwise control-state constraints [J].

Roesch, A. ;

Troeltzsch, F. .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (02) :548-564

[9] On the method of Lavrentiev regularization for nonlinear ill-posed problems [J].

Tautenhahn, U .

INVERSE PROBLEMS, 2002, 18 (01) :191-207

[10] Regular Lagrange multipliers for control problems with mixed pointwise control-state constraints [J].

Tröltzsch, F .

SIAM JOURNAL ON OPTIMIZATION, 2005, 15 (02) :616-634

← 1 →