{"title":"零potent Lie 群上不变控制系统的分散性和可控性","authors":"Jean G. Silva, Josiney A. Souza","doi":"10.1007/s13163-024-00500-w","DOIUrl":null,"url":null,"abstract":"<p>This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.</p>","PeriodicalId":501429,"journal":{"name":"Revista Matemática Complutense","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dispersiveness and controllability of invariant control systems on nilpotent Lie groups\",\"authors\":\"Jean G. Silva, Josiney A. Souza\",\"doi\":\"10.1007/s13163-024-00500-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.</p>\",\"PeriodicalId\":501429,\"journal\":{\"name\":\"Revista Matemática Complutense\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matemática Complutense\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13163-024-00500-w\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Matemática Complutense","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13163-024-00500-w","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Dispersiveness and controllability of invariant control systems on nilpotent Lie groups
This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.
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