连续时间线性二次最优控制问题收费公路性质与耗散率的关系

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2021-03-01 DOI:10.3934/MCRF.2020032

L. Grüne, Roberto Guglielmi

{"title":"连续时间线性二次最优控制问题收费公路性质与耗散率的关系","authors":"L. Grüne, Roberto Guglielmi","doi":"10.3934/MCRF.2020032","DOIUrl":null,"url":null,"abstract":"The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelty of these results is the possibility to encompass the presence of state and input constraints.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"24 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems\",\"authors\":\"L. Grüne, Roberto Guglielmi\",\"doi\":\"10.3934/MCRF.2020032\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelty of these results is the possibility to encompass the presence of state and input constraints.\",\"PeriodicalId\":48889,\"journal\":{\"name\":\"Mathematical Control and Related Fields\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2021-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Control and Related Fields\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/MCRF.2020032\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Control and Related Fields","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/MCRF.2020032","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 24

摘要

本文研究了连续时间有限维线性二次最优控制问题中收费公路现象与严格耗散性之间的关系。我们用与线性二次问题相关的系统矩阵来描述动力学的严格耗散性质。这些表征然后导致考虑的收费公路性质的新的必要条件，从而最终得到谱准则和矩阵不等式方面的必要和充分条件。这些结果的一个关键新颖之处在于可以包含状态和输入约束的存在。

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

On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems

The paper is devoted to analyze the connection between turnpike phenomena and strict dissipativity properties for continuous-time finite dimensional linear quadratic optimal control problems. We characterize strict dissipativity properties of the dynamics in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelty of these results is the possibility to encompass the presence of state and input constraints.

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

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.