{"title":"辛几何和最优性的必要条件","authors":"A. Agrachev, R. Gamkrelidze","doi":"10.1070/SM1992V072N01ABEH002137","DOIUrl":null,"url":null,"abstract":"With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"SYMPLECTIC GEOMETRY AND NECESSARY CONDITIONS FOR OPTIMALITY\",\"authors\":\"A. Agrachev, R. Gamkrelidze\",\"doi\":\"10.1070/SM1992V072N01ABEH002137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V072N01ABEH002137\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V072N01ABEH002137","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SYMPLECTIC GEOMETRY AND NECESSARY CONDITIONS FOR OPTIMALITY
With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.
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