{"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}
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.
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.
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