带有砰砰控制的纳维-斯托克斯速度跟踪问题的稳定性分析

IF 1.6 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Optimization Theory and Applications Pub Date : 2024-04-07 DOI:10.1007/s10957-024-02413-6

Alberto Domínguez Corella, Nicolai Jork, Šárka Nečasová, John Sebastian H. Simon

{"title":"带有砰砰控制的纳维-斯托克斯速度跟踪问题的稳定性分析","authors":"Alberto Domínguez Corella, Nicolai Jork, Šárka Nečasová, John Sebastian H. Simon","doi":"10.1007/s10957-024-02413-6","DOIUrl":null,"url":null,"abstract":"<p>This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier–Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem.</p>","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"12 1","pages":""},"PeriodicalIF":1.6000,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability analysis of the Navier–Stokes velocity tracking problem with bang-bang controls\",\"authors\":\"Alberto Domínguez Corella, Nicolai Jork, Šárka Nečasová, John Sebastian H. Simon\",\"doi\":\"10.1007/s10957-024-02413-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier–Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem.</p>\",\"PeriodicalId\":50100,\"journal\":{\"name\":\"Journal of Optimization Theory and Applications\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2024-04-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Optimization Theory and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10957-024-02413-6\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Optimization Theory and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10957-024-02413-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文主要研究与二维纳维-斯托克斯方程相关的速度跟踪问题解的稳定性。所考虑的最优控制问题在成本中不包含任何正则，因此可以预期会出现 "砰砰 "解。我们研究了考虑到跟踪数据和状态初始条件不确定性的扰动，并分析了当原始问题通过 Tikhonov 项正则化时的解收敛速率。稳定性分析依赖于最优映射的赫尔德次规则性，而赫尔德次规则性源于问题的必要条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stability analysis of the Navier–Stokes velocity tracking problem with bang-bang controls

This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier–Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence bang-bang solutions can be expected. We investigate perturbations that account for uncertainty in the tracking data and the initial condition of the state, and analyze the convergence rate of solutions when the original problem is regularized by the Tikhonov term. The stability analysis relies on the Hölder subregularity of the optimality mapping, which stems from the necessary conditions of the problem.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Optimization Theory and Applications 数学-应用数学

CiteScore

3.30

自引率

5.30%

发文量

149

审稿时长

9.9 months

期刊介绍： The Journal of Optimization Theory and Applications is devoted to the publication of carefully selected regular papers, invited papers, survey papers, technical notes, book notices, and forums that cover mathematical optimization techniques and their applications to science and engineering. Typical theoretical areas include linear, nonlinear, mathematical, and dynamic programming. Among the areas of application covered are mathematical economics, mathematical physics and biology, and aerospace, chemical, civil, electrical, and mechanical engineering.