{"title":"Boundary disturbance rejection for Caputo-Hadamard fractional heat equations via ADRC approach","authors":"Rui-Yang Cai , Hua-Cheng Zhou","doi":"10.1016/j.chaos.2024.115741","DOIUrl":null,"url":null,"abstract":"<div><div>This paper focuses on the boundary control matched disturbance rejection problem for Caputo-Hadamard fractional heat equations with time delay. By utilizing the novel idea of the active disturbance rejection control (ADRC) approach, two infinite-dimensional systems are constructed. One separates the disturbance from the control input, and the other estimates the unknown disturbance without high gain. By employing the backstepping method, together with the disturbance-compensator, a desired stabilizing controller is designed, and the asymptotical stability is achieved for the original system.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"189 ","pages":"Article 115741"},"PeriodicalIF":5.3000,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077924012931","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper focuses on the boundary control matched disturbance rejection problem for Caputo-Hadamard fractional heat equations with time delay. By utilizing the novel idea of the active disturbance rejection control (ADRC) approach, two infinite-dimensional systems are constructed. One separates the disturbance from the control input, and the other estimates the unknown disturbance without high gain. By employing the backstepping method, together with the disturbance-compensator, a desired stabilizing controller is designed, and the asymptotical stability is achieved for the original system.
期刊介绍：
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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