Luenberger observers for discrete-time nonlinear systems
Luenberger observers for discrete-time nonlinear systems
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离散时间非线性系统的 Luenberger 观测器
DOI：
10.1109/cdc40024.2019.9029220
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
U. Serres
中科院分区：
文献类型：
--
作者：
L. Brivadis;V. Andrieu;U. Serres
在本文中，我们考虑遵循 Luenberger 的原始想法，为离散时间非线性动力系统设计渐近观测器的问题。这种方法是一个两步设计过程。第一步，问题是估计状态函数。通过反转该映射获得状态估计。与连续时间背景一样，我们表明，只要引入由输出馈送的线性且稳定的离散时间系统，第一步总是可能的。基于弱可观测性假设，表明当稳定辅助系统的维数选取足够大时，状态估计函数是可逆的。该方法在具有多项式输出的线性系统上进行了说明。还研究了在连续时间情况下获得的与 Luenberger 观察者的联系。
In this paper, we consider the problem of designing an asymptotic observer for a nonlinear dynamical system in discrete-time following Luenberger’s original idea. This approach is a two-step design procedure. In a first step, the problem is to estimate a function of the state. The state estimation is obtained by inverting this mapping. As in the continuous-time context, we show that the first step is always possible provided a linear and stable discrete-time system fed by the output is introduced. Based on a weak observability assumption, it is shown that picking the dimension of the stable auxiliary system sufficiently large, the estimated function of the state is invertible. This approach is illustrated on linear systems with polynomial output. The link with the Luenberger observer obtained in the continuous-time case is also investigated.