{"title":"合成最佳稳定仿射系统","authors":"L. T. Ashchepkov","doi":"10.1134/s0965542524020039","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear and nonlinear systems is discussed.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Synthesis of an Optimal Stable Affine System\",\"authors\":\"L. T. Ashchepkov\",\"doi\":\"10.1134/s0965542524020039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear and nonlinear systems is discussed.</p>\",\"PeriodicalId\":55230,\"journal\":{\"name\":\"Computational Mathematics and Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Mathematics and Mathematical Physics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0965542524020039\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524020039","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A method for constructing a feedback that ensures the attraction of trajectories of an affine system to an equilibrium state and to a given manifold is proposed. The feedback is found in an analytical form as a solution to an auxiliary optimal control problem. Sufficient conditions for the existence of the optimal control are given. Application of the proposed method to some classes of linear and nonlinear systems is discussed.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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