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Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance
Zhou, Hua-Cheng1; Lv, Chunwan2; Guo, Bao-Zhu2,3,4; Chen, YangQuan5
2019-09-10
Source PublicationINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
ISSN1049-8923
Volume29Issue:13Pages:4384-4401
AbstractThis paper addresses the Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control subject to the control matched disturbance. The active disturbance rejection control (ADRC) approach is adopted for developing the control law. A state-feedback scheme is designed to estimate the disturbance by constructing two auxiliary systems: One is to separate the disturbance from the original system to a Mittag-Leffler stable system and the other is to estimate the disturbance finally. The proposed control law compensates the disturbance using its estimation and stabilizes system asymptotically. The closed-loop system is shown to be Mittag-Leffler stable and the constructed auxiliary systems in the closed loop are proved to be bounded. This is the first time for ADRC to be applied to a system described by the fractional partial differential system without using the high gain.
Keywordactive disturbance rejection control (ADRC) Mittag-Leffler stabilization time-fractional anomalous diffusion equation
DOI10.1002/rnc.4632
Language英语
WOS Research AreaAutomation & Control Systems ; Engineering ; Mathematics
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic ; Mathematics, Applied
WOS IDWOS:000478620500007
PublisherWILEY
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35353
Collection中国科学院数学与系统科学研究院
Corresponding AuthorZhou, Hua-Cheng
Affiliation1.Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China
2.Foshan Univ, Sch Math & Big Data, Foshan, Peoples R China
3.North China Elect Power Univ, Sch Math & Phys, Beijing, Peoples R China
4.Acad Sinica, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing, Peoples R China
5.Univ Calif Merced, MESA Lab, Merced, CA USA
Recommended Citation
GB/T 7714
Zhou, Hua-Cheng,Lv, Chunwan,Guo, Bao-Zhu,et al. Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance[J]. INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,2019,29(13):4384-4401.
APA Zhou, Hua-Cheng,Lv, Chunwan,Guo, Bao-Zhu,&Chen, YangQuan.(2019).Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance.INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL,29(13),4384-4401.
MLA Zhou, Hua-Cheng,et al."Mittag-Leffler stabilization for an unstable time-fractional anomalous diffusion equation with boundary control matched disturbance".INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 29.13(2019):4384-4401.
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