Backstepping observers for linear PDEs on higher-dimensional spatial domains

Jadachowski, Lukas, Meurer, Thomas and Kugi, Andreas (2015) Backstepping observers for linear PDEs on higher-dimensional spatial domains Automatica, 51 . pp. 85-97.

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Abstract

The extension of the backstepping-based state observer design is considered for systems governed by parabolic PDEs defined on a higher-dimensional cuboidal spatial domain with the measured output being restricted to a single boundary hyperplane. Thereby, a suitable coordinate and state transformation is employed, which allows for the application of the backstepping method for the determination of a Luenberger-type state observer with observer corrections entering the PDE and the boundary condition. This ensures that the observer error dynamics follows the behavior of a predefined exponentially stable target system. In view of a practical realization of the proposed observer approach, the idealized system output, previously assumed as measurable on the entire boundary hyperplane, is reconstructed from a limited set of optimally located measurements by means of a least squares approximation. The observer error convergence and the applicability of the proposed approach are confirmed analytically and are evaluated in numerical simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Document Type: Article
Additional Information: Times Cited: 3
Research affiliation: Kiel University
OceanRep > The Future Ocean - Cluster of Excellence
Refereed: Yes
ISSN: 0005-1098
Projects: Future Ocean
Date Deposited: 18 Oct 2016 03:45
Last Modified: 23 May 2017 12:14
URI: http://eprints.uni-kiel.de/id/eprint/32528

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