{"title":"Engel群上Sub-Finsler问题的Bang-Bang极值","authors":"Y. Sachkov","doi":"10.1109/STAB49150.2020.9140542","DOIUrl":null,"url":null,"abstract":"We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.","PeriodicalId":166223,"journal":{"name":"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Bang-Bang Extremals in Sub-Finsler Problems on Engel Group\",\"authors\":\"Y. Sachkov\",\"doi\":\"10.1109/STAB49150.2020.9140542\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.\",\"PeriodicalId\":166223,\"journal\":{\"name\":\"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)\",\"volume\":\"12 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2020 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/STAB49150.2020.9140542\",\"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 15th International Conference on Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference) (STAB)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/STAB49150.2020.9140542","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Bang-Bang Extremals in Sub-Finsler Problems on Engel Group
We consider a one-parameter family of left-invariant rank 2 sub-Finsler problems on the Engel group with the set of control parameters given by a square centered at the origin and rotated by an arbitrary angle. We describe the phase portrait for bang-bang extremals. Further, we obtain an upper bound on the number of bang arcs on optimal bang-bang extremals.
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