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Observer Design and Exponential Stabilization for Wave Equation in Energy Space by Boundary Displacement Measurement Only
Feng, Hongyinping1; Guo, Bao-Zhu2,3
2017-03-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume62Issue:3Pages:1438-1444
AbstractIn this technical note, we consider finite-time and exponential stabilization for one-dimensional wave equations by boundary displacement measurement only. We limit ourselves in the energy state space where the usual observability inequality is not valid anymore. However, in the optimal state space, the boundary displacement is indeed exactly observable. This motivates us to design observer via displacement output only for these systems. We first discuss a simple case as a motivation. An observer is designed and an output feedback control is then synthesized to make system finite-time stable in energy space. In this same spirit, we consider the same problem for an unstable wave equation and the finite-time stability is also achieved by displacement output feedback. Finally, we consider an anti-stable wave equation. A direct delayed output feedback control can achieve exponential stability with arbitrary decay rate. Simulation results are presented to validate the theoretical conclusions.
KeywordBoundary control exact observability finite-time stability observer wave equation
DOI10.1109/TAC.2016.2572122
Language英语
Funding ProjectNational Natural Science Foundation of China[61403239] ; Science Council of Shanxi Province[2015021010] ; National Research Foundation of South Africa
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000395924300033
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24737
Collection系统科学研究所
Corresponding AuthorFeng, Hongyinping; Guo, Bao-Zhu
Affiliation1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
2.Acad Sinica, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
3.Univ Witwatersrand, Sch Comp Sci & Appl Math, ZA-2050 Johannesburg, South Africa
Recommended Citation
GB/T 7714
Feng, Hongyinping,Guo, Bao-Zhu. Observer Design and Exponential Stabilization for Wave Equation in Energy Space by Boundary Displacement Measurement Only[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2017,62(3):1438-1444.
APA Feng, Hongyinping,&Guo, Bao-Zhu.(2017).Observer Design and Exponential Stabilization for Wave Equation in Energy Space by Boundary Displacement Measurement Only.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,62(3),1438-1444.
MLA Feng, Hongyinping,et al."Observer Design and Exponential Stabilization for Wave Equation in Energy Space by Boundary Displacement Measurement Only".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 62.3(2017):1438-1444.
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