{"title":"奇异扰动优化跟踪问题","authors":"V. A. Sobolev","doi":"10.1134/s0012266124040116","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a singularly perturbed optimal tracking problem with a given reference path\nin the case of incomplete information about the state vector in the presence of exogenous\ndisturbances. To analyze the differential equations that arise when solving this problem, we use\nthe decomposition method, which is based on the technique of integral manifolds of fast and slow\nmotions.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"68 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Singularly Perturbed Optimal Tracking Problem\",\"authors\":\"V. A. Sobolev\",\"doi\":\"10.1134/s0012266124040116\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We consider a singularly perturbed optimal tracking problem with a given reference path\\nin the case of incomplete information about the state vector in the presence of exogenous\\ndisturbances. To analyze the differential equations that arise when solving this problem, we use\\nthe decomposition method, which is based on the technique of integral manifolds of fast and slow\\nmotions.\\n</p>\",\"PeriodicalId\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"68 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124040116\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124040116","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We consider a singularly perturbed optimal tracking problem with a given reference path
in the case of incomplete information about the state vector in the presence of exogenous
disturbances. To analyze the differential equations that arise when solving this problem, we use
the decomposition method, which is based on the technique of integral manifolds of fast and slow
motions.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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