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.
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页码：1328 / 1354
页数：27
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