{"title":"On the Problem of Controlling a Nonlinear System by a Discrete Control under Disturbance","authors":"K. A. Shchelchkov","doi":"10.1134/s0012266124010105","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the problem of stabilization to zero under disturbance in terms of\na differential pursuit game. The dynamics is described by a nonlinear autonomous system of\ndifferential equations. The set of control values of the pursuer is finite, and that of the evader\n(disturbance) is a compact set. The control objective, i.e., the pursuer’s goal, is to bring the\ntrajectory to any predetermined neighborhood of zero in finite time regardless of the disturbance.\nTo construct the control, the pursuer knows only the state coordinates at some discrete times, and\nthe choice of the disturbance’s control is unknown. In the paper, we obtain conditions for the\nexistence of a neighborhood of zero from each point of which a capture occurs in the indicated\nsense. A winning control is constructed constructively and has an additional property specified in\na theorem. In addition, an estimate of the capture time sharp in some sense is produced.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","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/s0012266124010105","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 the problem of stabilization to zero under disturbance in terms of
a differential pursuit game. The dynamics is described by a nonlinear autonomous system of
differential equations. The set of control values of the pursuer is finite, and that of the evader
(disturbance) is a compact set. The control objective, i.e., the pursuer’s goal, is to bring the
trajectory to any predetermined neighborhood of zero in finite time regardless of the disturbance.
To construct the control, the pursuer knows only the state coordinates at some discrete times, and
the choice of the disturbance’s control is unknown. In the paper, we obtain conditions for the
existence of a neighborhood of zero from each point of which a capture occurs in the indicated
sense. A winning control is constructed constructively and has an additional property specified in
a theorem. In addition, an estimate of the capture time sharp in some sense is produced.
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