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Approximate observability and back and forth observer of a PDE model of crystallisation process

Abstract : In this paper, we are interested in the estimation of Particle Size Distributions (PSDs) during a batch crystallization process in which particles of two different shapes coexist and evolve simultaneously. The PSDs are estimated thanks to a measurement of an apparent Chord Length Distribution (CLD), a measure that we model for crystals of spheroidal shape. Our main result is to prove the approximate observability of the infinite-dimensional system in any positive time. Under this observability condition, we are able to apply a Back and Forth Nudging (BFN) algorithm to reconstruct the PSD.
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https://hal.archives-ouvertes.fr/hal-03175017
Contributor : Ludovic Sacchelli <>
Submitted on : Friday, March 19, 2021 - 4:43:31 PM
Last modification on : Tuesday, March 23, 2021 - 3:30:04 AM

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  • HAL Id : hal-03175017, version 1
  • ARXIV : 2103.11656

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Lucas Brivadis, Ludovic Sacchelli. Approximate observability and back and forth observer of a PDE model of crystallisation process. 2021. ⟨hal-03175017⟩

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