具有快速振荡系数的carathacimodory微分夹杂半轴上最优控制问题的渐近分析

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2023-10-27 DOI:10.15388/namc.2023.28.33435

Sergey Dashkovskiy, Oleksiy Kapustyan, Olena Kapustian, Tetyana Zhuk

{"title":"具有快速振荡系数的carathacimodory微分夹杂半轴上最优控制问题的渐近分析","authors":"Sergey Dashkovskiy, Oleksiy Kapustyan, Olena Kapustian, Tetyana Zhuk","doi":"10.15388/namc.2023.28.33435","DOIUrl":null,"url":null,"abstract":"We consider an optimal control problem for a differential inclusion of the Carathéodory type affine with respect to the control with a coercive cost functional on a semiaxis and with fast oscillating time-dependent coefficients. We prove that, when the small parameter converges to zero, the solution to this problem tends to some solution of the optimal control problem with averaged coefficients, where the averaging we understand in the sense of the Kuratowski upper limit.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"277 6","pages":"0"},"PeriodicalIF":2.6000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic analysis of optimal control problems on the semiaxes for Carathéodory differential inclusions with fast oscillating coefficients\",\"authors\":\"Sergey Dashkovskiy, Oleksiy Kapustyan, Olena Kapustian, Tetyana Zhuk\",\"doi\":\"10.15388/namc.2023.28.33435\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider an optimal control problem for a differential inclusion of the Carathéodory type affine with respect to the control with a coercive cost functional on a semiaxis and with fast oscillating time-dependent coefficients. We prove that, when the small parameter converges to zero, the solution to this problem tends to some solution of the optimal control problem with averaged coefficients, where the averaging we understand in the sense of the Kuratowski upper limit.\",\"PeriodicalId\":49286,\"journal\":{\"name\":\"Nonlinear Analysis-Modelling and Control\",\"volume\":\"277 6\",\"pages\":\"0\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2023-10-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Modelling and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15388/namc.2023.28.33435\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Modelling and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15388/namc.2023.28.33435","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们考虑了一个关于半轴上具有强制代价泛函且具有快速振荡时间相关系数的控制的微分包含的carathimodory型仿射的最优控制问题。证明了当小参数收敛于零时，该问题的解趋向于具有平均系数的最优控制问题的某个解，其中的平均我们理解为Kuratowski上限的意义。

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

Asymptotic analysis of optimal control problems on the semiaxes for Carathéodory differential inclusions with fast oscillating coefficients

We consider an optimal control problem for a differential inclusion of the Carathéodory type affine with respect to the control with a coercive cost functional on a semiaxis and with fast oscillating time-dependent coefficients. We prove that, when the small parameter converges to zero, the solution to this problem tends to some solution of the optimal control problem with averaged coefficients, where the averaging we understand in the sense of the Kuratowski upper limit.

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

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.