结晶过程PDE模型的近似能观性和来回观测器
Approximate observability and back and forth observer of a PDE model of crystallisation process
摘要：
在本文中，我们感兴趣的是在间歇结晶过程中，两种不同形状的颗粒共存，并同时演变的粒度分布（PSD）的估计。PSD是通过测量表观弦长分布（CLD）来估计的，CLD是我们为球形晶体建模的一种测量方法。我们的主要结果是证明了无穷维系统在任意正时间的近似可观性。在此可观测性条件下，我们能够应用一个来回轻推（BFN）算法来重建PSD。
英文摘要：
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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