{"title":"On Piecewise Cubic Estimates of the Value Function in a Target Control Problem for a Nonlinear System","authors":"P. A. Tochilin, I. A. Chistyakov","doi":"10.1134/s0012266124050082","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A nonlinear system of ordinary differential equations with control parameters is considered.\nPointwise restrictions are imposed on the possible values of these parameters. It is required to\nsolve the problem of transferring the trajectory of the system from an arbitrary initial position to\nthe smallest possible neighborhood of a given target set on a fixed time interval by selecting an\nappropriate feedback control. To solve this problem, it is proposed to construct a continuous\npiecewise cubic function of a special kind. The level sets of this function correspond to internal\nestimates of the solvability sets of the system. Using this function, it is also possible to construct a\nfeedback control function that solves the target control problem on a fixed time interval. The\npaper proposes formulas for calculating the values of the piecewise cubic function, examines its\nproperties, and considers an algorithm for searching for parameters defining this function.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050082","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A nonlinear system of ordinary differential equations with control parameters is considered.
Pointwise restrictions are imposed on the possible values of these parameters. It is required to
solve the problem of transferring the trajectory of the system from an arbitrary initial position to
the smallest possible neighborhood of a given target set on a fixed time interval by selecting an
appropriate feedback control. To solve this problem, it is proposed to construct a continuous
piecewise cubic function of a special kind. The level sets of this function correspond to internal
estimates of the solvability sets of the system. Using this function, it is also possible to construct a
feedback control function that solves the target control problem on a fixed time interval. The
paper proposes formulas for calculating the values of the piecewise cubic function, examines its
properties, and considers an algorithm for searching for parameters defining this function.
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