论文标题
无限维系统的Luenberger观察者，来回轻推并应用于结晶过程
Luenberger observers for infinite-dimensional systems, Back and Forth Nudging and application to a crystallization process
论文作者
论文摘要
本文讨论了与时变线性无限维系统的观察者设计问题。我们既可以通过渐近观察者从输出对系统状态的在线估算问题进行解决，又解决了通过来回裸（BFN）算法对初始状态估算的离线估计问题。在这两种情况下，我们在弱的可检测性假设下表明，类似Luenberger的观察者可以重建系统的所谓可观察子空间。但是，由于不需要确切的可观察性假设，因此总体上只有观察者的弱收敛性。需要系统上的其他条件以显示强大的收敛性。我们将结果应用于由具有周期性边界条件的一维运输方程建模的批处理结晶过程，在该方程中，我们试图估算和弦长度分布的晶体尺寸分布。
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.
