OPTIMAL CONTROL OF SEMILINEAR PARABOLIC EQUATIONS BY BV-FUNCTIONS

被引：18

作者：

Casas, Eduardo ^{[1
]}

Kruse, Florian ^{[2
]}

Kunisch, Karl ^{[2
]}

机构：

[1] Univ Cantabria, Dept Matemat Aplicada & Ciencias Comp, ETSI Ind & Telecomunicac, E-39005 Santander, Spain

[2] Karl Franzens Univ Graz, Inst Math & Sci Comp, Heinrichstr 36, A-8010 Graz, Austria

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2017年 / 55卷 / 03期

基金：

奥地利科学基金会;

关键词：

bounded variation functions; optimal control; sparsity; semilinear parabolic equations; first and second order optimality conditions; discontinuous Galerkin approximations; ELLIPTIC CONTROL-PROBLEMS; DIRECTIONAL SPARSITY; MEASURE-SPACES; DISCRETIZATION; APPROXIMATION;

D O I：

10.1137/16M1056511

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Optimal control problems for semilinear parabolic equations with control costs involving the total bounded variation seminorm are analyzed. This choice of control cost favors optimal controls which are piecewise constant and it penalizes the number of jumps. It is an appropriate choice if a simple structure of the optimal controls is desired, which, however, is still sufficiently flexible so that good tracking properties can be maintained. Existence of optimal controls, necessary and sufficient optimality conditions, and sparsity properties of the derivatives are obtained. Convergence of a finite element approximation is analyzed and numerical examples illustrating structural properties of the optimal controls are provided.

引用

页码：1752 / 1788

页数：37

共 24 条

[1]

Ambrosio L., 2000, OX MATH M, pxviii, DOI [10.1017/S0024609301309281, 10.1093/oso/9780198502456.001.0001]

[2]

[Anonymous], 2006, SPRINGER SER COMPUT

[3]

[Anonymous], 1997, MATH SURVEYS MONOGR

[4] Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations [J].

Casas, E .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1997, 35 (04) :1297-1327

[5] Second-Order Optimality Conditions for Weak and Strong Local Solutions of Parabolic Optimal Control Problems [J].

Casas E. ;

Tröltzsch F. .

Vietnam Journal of Mathematics, 2016, 44 (1) :181-202

[6] APPROXIMATION OF OPTIMAL CONTROL PROBLEMS IN THE COEFFICIENT FOR THE p-LAPLACE EQUATION. I. CONVERGENCE RESULT [J].

Casas, Eduardo ;

Kogut, Peter I. ;

Leugering, Guenter .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (03) :1406-1422

[7] OPTIMAL CONTROL OF SEMILINEAR ELLIPTIC EQUATIONS IN MEASURE SPACES [J].

Casas, Eduardo ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2014, 52 (01) :339-364

[8] PARABOLIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS [J].

Casas, Eduardo ;

Clason, Christian ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (01) :28-63

[9] APPROXIMATION OF ELLIPTIC CONTROL PROBLEMS IN MEASURE SPACES WITH SPARSE SOLUTIONS [J].

Casas, Eduardo ;

Clason, Christian ;

Kunisch, Karl .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2012, 50 (04) :1735-1752

[10] SECOND ORDER ANALYSIS FOR OPTIMAL CONTROL PROBLEMS: IMPROVING RESULTS EXPECTED FROM ABSTRACT THEORY [J].

Casas, Eduardo ;

Troeltzsch, Fredi .

SIAM JOURNAL ON OPTIMIZATION, 2012, 22 (01) :261-279

← 1 2 3 →