Abstract

In this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice of the observer gain and using positive bounded perturbation results. We show in particular that the error of the state estimation converges exponentially to zero. Finally, the main result is applied to an isothermal tubular (bio) reactor model, namely the plug-flow (bio) reactor model. The approach is illustrated by some numerical simulations.

中文翻译：

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Hilbert格空间中线性正系统的正观测器

摘要

在这项工作中，我们研究为一类无限维线性正系统设计一个正观测器的问题。我们提出了一种基于经典Luenberger式观察器的新观察器设计。提议的观察员是积极的。即，它确保状态估计在任何时候都是非负的。通过选择特定的观察者增益并使用正有界扰动结果证明了这种积极的观察者的存在。我们特别表明，状态估计的误差呈指数收敛至零。最后，将主要结果应用于等温管式（生物）反应器模型，即活塞流（生物）反应器模型。一些数值模拟说明了该方法。