{"title":"On a Problem of Calculating the Solvability Set for a Linear System with Uncertainty","authors":"A. A. Melnikova, P. A. Tochilin","doi":"10.1134/s00122661230110083","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a linear-convex control system defined by a set of differential equations with\ncontinuous matrix coefficients. The system may have control parameters, as well as uncertainties\n(interference) the possible values of which are subject to strict pointwise constraints. For this\nsystem, over a finite period of time, taking into account the constraints, we study the problem of\nguaranteed hitting the target set from a given initial position despite the effect of uncertainty. The\nmain stage of solving the problem is the construction of an alternating integral and a solvability\nset. To construct the latter, the greatest computational complexity is the calculation of the\ngeometric difference between the target set and the set determined by the uncertainty. A\ntwo-dimensional example of this problem is considered for which a method is proposed for finding\nthe solvability set without the need to calculate the convex hull of the difference of the support\nfunctions of the sets.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-29","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/s00122661230110083","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
We consider a linear-convex control system defined by a set of differential equations with
continuous matrix coefficients. The system may have control parameters, as well as uncertainties
(interference) the possible values of which are subject to strict pointwise constraints. For this
system, over a finite period of time, taking into account the constraints, we study the problem of
guaranteed hitting the target set from a given initial position despite the effect of uncertainty. The
main stage of solving the problem is the construction of an alternating integral and a solvability
set. To construct the latter, the greatest computational complexity is the calculation of the
geometric difference between the target set and the set determined by the uncertainty. A
two-dimensional example of this problem is considered for which a method is proposed for finding
the solvability set without the need to calculate the convex hull of the difference of the support
functions of the sets.
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