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Hokkaido University Collection of Scholarly and Academic Papers >
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Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages
| Title: | Backstepping observer design for parabolic PDEs with measurement of weighted spatial averages |
| Authors: | Tsubakino, Daisuke Browse this author | | Hara, Shinji Browse this author |
| Keywords: | Distributed-parameter systems | | Observers | | Backstepping | | Parabolic partial differential equations | | Spatial averages |
| Issue Date: | 9-Mar-2015 |
| Publisher: | Pergamon Press |
| Journal Title: | Automatica |
| Volume: | 53 |
| Start Page: | 179 |
| End Page: | 187 |
| Publisher DOI: | 10.1016/j.automatica.2014.12.019 |
| Abstract: | This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/58044 |
| Appears in Collections: | 情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 椿野 大輔
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