{"title":"Stabilization of a Chain of Three Integrators Subject to a Phase Constraint","authors":"A. V. Pesterev, Yu. V. Morozov","doi":"10.1134/S0005117924700036","DOIUrl":null,"url":null,"abstract":"<p>The problem of stabilizing a chain of three integrators subject to a phase constraint is studied. Continuous constrained control in the form of nested sigmoids, which guarantees the fulfillment of the phase constraint, is synthesized. A Lyapunov function is constructed, and necessary and sufficient conditions of global stability of the closed-loop system are established. The discussion is illustrated by numerical examples.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automation and Remote Control","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1134/S0005117924700036","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The problem of stabilizing a chain of three integrators subject to a phase constraint is studied. Continuous constrained control in the form of nested sigmoids, which guarantees the fulfillment of the phase constraint, is synthesized. A Lyapunov function is constructed, and necessary and sufficient conditions of global stability of the closed-loop system are established. The discussion is illustrated by numerical examples.
期刊介绍：
Automation and Remote Control is one of the first journals on control theory. The scope of the journal is control theory problems and applications. The journal publishes reviews, original articles, and short communications (deterministic, stochastic, adaptive, and robust formulations) and its applications (computer control, components and instruments, process control, social and economy control, etc.).
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