Selivanov, A. orcid.org/0000-0001-5075-7229 and Fridman, E. (2018) Delayed boundary control of a heat equation under discrete-time point measurements. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC). 2017 IEEE 56th Annual Conference on Decision and Control (CDC), 12-15 Dec 2017, Melbourne, VIC, Australia. IEEE , pp. 1248-1253. ISBN 9781509028740
Abstract
We consider a reaction-diffusion PDE under continuously applied boundary control that contains a constant delay. The point measurements are sampled in time and transmitted through a network with a time-varying delay. We construct an observer that predicts the value of the state allowing to compensate for the constant boundary delay. Using a time-varying injection gain, we ensure that the estimation error vanishes exponentially with a desired decay rate if the delays and sampling intervals are small enough while the number of sensors is large enough. The stability conditions, obtained via a Lyapunov-Krasovskii functional, are formulated in terms of linear matrix inequalities. By applying the backstepping transformation to the future state estimation, we derive a boundary controller that guarantees the exponential stability of the closed-loop system with an arbitrary decay rate smaller than that of the observer. The results are demonstrated by an example.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Nov 2019 12:13 |
Last Modified: | 15 Nov 2019 15:27 |
Published Version: | https://ieeexplore.ieee.org/abstract/document/8263... |
Status: | Published |
Publisher: | IEEE |
Refereed: | Yes |
Identification Number: | 10.1109/CDC.2017.8263827 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:153381 |