{"title":"On converse zeroing barrier functions","authors":"Ziliang Lyu , Xiangru Xu , Yiguang Hong , Lihua Xie","doi":"10.1016/j.automatica.2024.112011","DOIUrl":null,"url":null,"abstract":"<div><div>The paper studies the safety verification problem for nonlinear systems and focuses on the converse problem of zeroing barrier functions (ZBFs). We establish two necessary and sufficient conditions for the existence of a ZBF by solving the converse ZBF problem. Moreover, we also consider exponential barrier functions (EBFs), a special case of the ZBF, and provide a necessary and sufficient condition for the existence of an EBF when the state trajectory, starting from the interior of the safe set, cannot visit the boundary within finite time.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"172 ","pages":"Article 112011"},"PeriodicalIF":4.8000,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automatica","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0005109824005053","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper studies the safety verification problem for nonlinear systems and focuses on the converse problem of zeroing barrier functions (ZBFs). We establish two necessary and sufficient conditions for the existence of a ZBF by solving the converse ZBF problem. Moreover, we also consider exponential barrier functions (EBFs), a special case of the ZBF, and provide a necessary and sufficient condition for the existence of an EBF when the state trajectory, starting from the interior of the safe set, cannot visit the boundary within finite time.
期刊介绍：
Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field.
After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience.
Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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