{"title":"Fixed-time stability for parabolic PDE","authors":"Anna Michalak","doi":"10.1016/j.ejcon.2025.101218","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we introduce a novel methodology for investigating the fixed-time stability properties of the zero solution to a semilinear parabolic equation. In pursuit of this, we introduce a novel dual approach to the Lyapunov concept of stability. The dual Lyapunov function adheres to a dual Hamilton–Jacobi inequality, forming the foundation for investigating fixed-time stability (fixed extinction time) in the original problem.</div></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":"83 ","pages":"Article 101218"},"PeriodicalIF":2.6000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0947358025000469","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/10 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce a novel methodology for investigating the fixed-time stability properties of the zero solution to a semilinear parabolic equation. In pursuit of this, we introduce a novel dual approach to the Lyapunov concept of stability. The dual Lyapunov function adheres to a dual Hamilton–Jacobi inequality, forming the foundation for investigating fixed-time stability (fixed extinction time) in the original problem.
期刊介绍：
The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field.
The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering.
The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications.
Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results.
The design and implementation of a successful control system requires the use of a range of techniques:
Modelling
Robustness Analysis
Identification
Optimization
Control Law Design
Numerical analysis
Fault Detection, and so on.
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