{"title":"约束连续系统最小时间函数的lipschitz性及其在可达性分析中的应用","authors":"M. Maghenem, R. Sanfelice","doi":"10.23919/ACC45564.2020.9147496","DOIUrl":null,"url":null,"abstract":"The minimal-time function with respect to a closed set for a constrained continuous-time system provides the first time that a solution starting from a given initial condition reaches that set. In this paper, we propose infinitesimal necessary and sufficient conditions for the minimal-time function to be locally Lipschitz. As an application of our results, we show that, in constrained continuous-time systems, the Lipschitz continuity of the minimal-time function with respect to the boundary of the set where the solutions are defined plays a crucial role on the Lipschitz continuity of the reachable set.","PeriodicalId":288450,"journal":{"name":"2020 American Control Conference (ACC)","volume":"138 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Lipschitzness of Minimal-Time Functions in Constrained Continuous-Time Systems with Applications to Reachability Analysis\",\"authors\":\"M. Maghenem, R. Sanfelice\",\"doi\":\"10.23919/ACC45564.2020.9147496\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The minimal-time function with respect to a closed set for a constrained continuous-time system provides the first time that a solution starting from a given initial condition reaches that set. In this paper, we propose infinitesimal necessary and sufficient conditions for the minimal-time function to be locally Lipschitz. As an application of our results, we show that, in constrained continuous-time systems, the Lipschitz continuity of the minimal-time function with respect to the boundary of the set where the solutions are defined plays a crucial role on the Lipschitz continuity of the reachable set.\",\"PeriodicalId\":288450,\"journal\":{\"name\":\"2020 American Control Conference (ACC)\",\"volume\":\"138 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2020 American Control Conference (ACC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23919/ACC45564.2020.9147496\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2020 American Control Conference (ACC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23919/ACC45564.2020.9147496","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Lipschitzness of Minimal-Time Functions in Constrained Continuous-Time Systems with Applications to Reachability Analysis
The minimal-time function with respect to a closed set for a constrained continuous-time system provides the first time that a solution starting from a given initial condition reaches that set. In this paper, we propose infinitesimal necessary and sufficient conditions for the minimal-time function to be locally Lipschitz. As an application of our results, we show that, in constrained continuous-time systems, the Lipschitz continuity of the minimal-time function with respect to the boundary of the set where the solutions are defined plays a crucial role on the Lipschitz continuity of the reachable set.