Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process

This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Fo...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2021-01, Vol.59 (2), p.857-886
Main Authors: Brivadis, Lucas, Andrieu, Vincent, Serres, Ulysse, Gauthier, Jean-Paul
Format: Article
Language:English
Subjects:
Automatic
Engineering Sciences
Mathematics
Optimization and Control
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Summary:This paper deals with the observer design problem for time-varying linear infinite-dimensional systems. We address both the problem of online estimation of the state of the system from the output via an asymptotic observer, and the problem of offline estimation of the initial state via a Back and Forth Nudging (BFN) algorithm. In both contexts, we show under a weak detectability assumption that a Luenberger-like observer may reconstruct the so-called observable subspace of the system. However, since no exact observability hypothesis is required, only a weak convergence of the observer holds in general. Additional conditions on the system are required to show the strong convergence. We provide an application of our results to a batch crystallization process modeled by a one-dimensional transport equation with periodic boundary conditions, in which we try to estimate the Crystal Size Distribution from the Chord Length Distribution.
ISSN:0363-0129
1095-7138
DOI:10.1137/20M1329020