{"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":50580,"journal":{"name":"Differential Equations","volume":"10 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050070","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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