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Luenberger Observers for Infinite-Dimensional Systems, Back and Forth Nudging, and Application to a Crystallization Process
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-03-02 , DOI: 10.1137/20m1329020 Lucas Brivadis , Vincent Andrieu , Ulysse Serres , Jean-Paul Gauthier
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-03-02 , DOI: 10.1137/20m1329020 Lucas Brivadis , Vincent Andrieu , Ulysse Serres , Jean-Paul Gauthier
SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 857-886, January 2021.
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 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.
中文翻译：
无限尺寸系统的Luenberger观测器，前后微动及其在结晶过程中的应用
SIAM控制与优化杂志，第59卷，第2期，第857-886页，2021年1月。
本文研究时变线性无限维系统的观测器设计问题。我们既解决了通过渐近观测器从输出对系统状态进行在线估计的问题，又解决了通过来回微动算法对初始状态进行离线估计的问题。在这两种情况下，我们都表明在弱可检测性假设下，类似Luenberger的观察者可以重建系统的所谓可观察子空间。但是，由于不需要精确的可观察性假设，因此通常只具有弱的观察者收敛性。需要系统上的其他条件才能显示出强大的收敛性。我们将结果应用到通过周期性边界条件的一维输运方程建模的批结晶过程中，
更新日期：2021-04-23
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 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.
中文翻译：
无限尺寸系统的Luenberger观测器，前后微动及其在结晶过程中的应用
SIAM控制与优化杂志，第59卷，第2期，第857-886页，2021年1月。
本文研究时变线性无限维系统的观测器设计问题。我们既解决了通过渐近观测器从输出对系统状态进行在线估计的问题，又解决了通过来回微动算法对初始状态进行离线估计的问题。在这两种情况下，我们都表明在弱可检测性假设下，类似Luenberger的观察者可以重建系统的所谓可观察子空间。但是，由于不需要精确的可观察性假设，因此通常只具有弱的观察者收敛性。需要系统上的其他条件才能显示出强大的收敛性。我们将结果应用到通过周期性边界条件的一维输运方程建模的批结晶过程中，
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