OPTIMAL CONTROL OF THE TWO-DIMENSIONAL STATIONARY NAVIER-STOKES EQUATIONS WITH MEASURE VALUED CONTROLS

被引：11

作者：

Casas, Eduardo ^{[1
]}

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 | 2019年 / 57卷 / 02期

基金：

欧盟地平线“2020”;

关键词：

Navier-Stokes equations; Borel measures; sparsity; first and second order optimality conditions; stability; PARABOLIC CONTROL-PROBLEMS; ELLIPTIC CONTROL-PROBLEMS; MEASURE-SPACES; 2ND-ORDER; APPROXIMATION;

D O I：

10.1137/18M1185582

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider an optimal control problem for the two-dimensional stationary Navier-Stokes system. Looking for sparsity, we take Borel measures as controls. We prove the well-posedness of the control problem and derive necessary and sufficient conditions for local optimality of the controls. Finally, under a second order condition, we prove rates of the optimal states with respect to small perturbations in the data of the control problem.

引用

页码：1328 / 1354

页数：27

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