{"title":"Prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems","authors":"Hui Wang , Wuquan Li , Miroslav Krstic","doi":"10.1016/j.sysconle.2024.105859","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems with nonlinear growth condition. Different from the existing scaling designs for nonlinear systems, we propose new non-scaling designs characterized by new scaled quadratic Lyapunov functions. The advantage of our design is that it is simpler and easier for implementation. We first design a controller to ensure that the equilibrium at the origin of the plant is prescribed-time stable. Then we redesign the controller and solve the prescribed-time inverse optimal stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, a simulation example is given to illustrate the designs.</p></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691124001476","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems with nonlinear growth condition. Different from the existing scaling designs for nonlinear systems, we propose new non-scaling designs characterized by new scaled quadratic Lyapunov functions. The advantage of our design is that it is simpler and easier for implementation. We first design a controller to ensure that the equilibrium at the origin of the plant is prescribed-time stable. Then we redesign the controller and solve the prescribed-time inverse optimal stabilization problem, with an infinite gain margin. Specifically, the designed controller is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. Finally, a simulation example is given to illustrate the designs.
期刊介绍：
Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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