{"title":"论非线性系统输入到状态组成安全的充分和必要条件","authors":"","doi":"10.1016/j.sysconle.2024.105886","DOIUrl":null,"url":null,"abstract":"<div><p>This paper is concerned with studying the problem of compositional input-to-state safety (ISSf) using input-to-state safe barrier functions (ISSf-BFs) for nonlinear systems given as an interconnection of subsystems. A sufficient condition is proposed to verify ISSf for nonlinear interconnected systems, which allows that only some subsystems are ISSf and the others are not. The idea behind the sufficient condition is to establish ISSf of nonlinear interconnected systems based on ISSf of some lower dimensional subsystems, in conjunction with a general type of interconnection between subsystems. Also, a necessary condition is derived by using additively separable ISSf-BFs, which provides a tool for analyzing ISSf of interconnected subsystems. Meanwhile, the necessary condition indicates that the ISSf problem of the overall nonlinear system can be divided into decoupled subproblems, which is dealt with less computational effort. In particular, a sufficient and necessary condition of compositional ISSf is obtained. Finally, three examples are presented to demonstrate the effectiveness of the theoretical results.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On sufficient and necessary conditions of compositional input-to-state safety for nonlinear systems\",\"authors\":\"\",\"doi\":\"10.1016/j.sysconle.2024.105886\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper is concerned with studying the problem of compositional input-to-state safety (ISSf) using input-to-state safe barrier functions (ISSf-BFs) for nonlinear systems given as an interconnection of subsystems. A sufficient condition is proposed to verify ISSf for nonlinear interconnected systems, which allows that only some subsystems are ISSf and the others are not. The idea behind the sufficient condition is to establish ISSf of nonlinear interconnected systems based on ISSf of some lower dimensional subsystems, in conjunction with a general type of interconnection between subsystems. Also, a necessary condition is derived by using additively separable ISSf-BFs, which provides a tool for analyzing ISSf of interconnected subsystems. Meanwhile, the necessary condition indicates that the ISSf problem of the overall nonlinear system can be divided into decoupled subproblems, which is dealt with less computational effort. In particular, a sufficient and necessary condition of compositional ISSf is obtained. Finally, three examples are presented to demonstrate the effectiveness of the theoretical results.</p></div>\",\"PeriodicalId\":49450,\"journal\":{\"name\":\"Systems & Control Letters\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-07-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Systems & Control Letters\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167691124001749\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124001749","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
On sufficient and necessary conditions of compositional input-to-state safety for nonlinear systems
This paper is concerned with studying the problem of compositional input-to-state safety (ISSf) using input-to-state safe barrier functions (ISSf-BFs) for nonlinear systems given as an interconnection of subsystems. A sufficient condition is proposed to verify ISSf for nonlinear interconnected systems, which allows that only some subsystems are ISSf and the others are not. The idea behind the sufficient condition is to establish ISSf of nonlinear interconnected systems based on ISSf of some lower dimensional subsystems, in conjunction with a general type of interconnection between subsystems. Also, a necessary condition is derived by using additively separable ISSf-BFs, which provides a tool for analyzing ISSf of interconnected subsystems. Meanwhile, the necessary condition indicates that the ISSf problem of the overall nonlinear system can be divided into decoupled subproblems, which is dealt with less computational effort. In particular, a sufficient and necessary condition of compositional ISSf is obtained. Finally, three examples are presented to demonstrate the effectiveness of the theoretical results.
期刊介绍:
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.