{"title":"Decomposition of Singularly Perturbed Optimal Tracking Problems with a Given Reference Trajectory","authors":"V. A. Sobolev","doi":"10.1134/S1990478923030171","DOIUrl":null,"url":null,"abstract":"<p> For the first time, the problem of optimal tracking with a given reference trajectory and\nan integral quadratic performance criterion in the presence of singular perturbations is considered.\nThe decomposition method is used to analyze singularly perturbed differential systems that arise\nin solving this problem. The method is based on the technique of integral manifolds of fast and\nslow motions. A suboptimal control is constructed the use of which leads to a difference in the\nvalues of the minimized functional for the optimal and suboptimal controls by an amount of the\norder of the second power of a small parameter characterizing singular perturbations.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"640 - 650"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923030171","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
For the first time, the problem of optimal tracking with a given reference trajectory and
an integral quadratic performance criterion in the presence of singular perturbations is considered.
The decomposition method is used to analyze singularly perturbed differential systems that arise
in solving this problem. The method is based on the technique of integral manifolds of fast and
slow motions. A suboptimal control is constructed the use of which leads to a difference in the
values of the minimized functional for the optimal and suboptimal controls by an amount of the
order of the second power of a small parameter characterizing singular perturbations.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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