{"title":"Backstepping Stabilization of Nonlinear Dynamical Systems under State Constraints","authors":"A. E. Golubev","doi":"10.1134/s0012266124050070","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The problem of stabilizing the zero value of the state vector of constrained nonlinear\ndynamical systems written in a special form is solved. The proposed control design accounts for\nmagnitude constraints on the values of state variables and is based on the integrator backstepping\napproach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in\ncontrast to similar known results, are based on the use of linear virtual stabilizing functions that\ndo not grow unboundedly as the state variables approach boundary values. As an example, we\nconsider a state constraints aware solution of the control problem of positioning an autonomous\nunderwater vehicle at a given point in space.\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/s0012266124050070","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
The problem of stabilizing the zero value of the state vector of constrained nonlinear
dynamical systems written in a special form is solved. The proposed control design accounts for
magnitude constraints on the values of state variables and is based on the integrator backstepping
approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in
contrast to similar known results, are based on the use of linear virtual stabilizing functions that
do not grow unboundedly as the state variables approach boundary values. As an example, we
consider a state constraints aware solution of the control problem of positioning an autonomous
underwater vehicle at a given point in space.
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