基于离散时间输出快照的离散系统状态估计问题

Shen Zeng, H. Ishii, F. Allgöwer
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引用次数: 8

摘要

我们考虑重构一组结构相同的LTI系统的初始状态的问题,在这种情况下,组中单个系统的输出测量是在离散时间步长以匿名方式接收的:虽然我们知道组中单个系统的所有输出测量,但我们不知道哪个输出测量对应于哪个系统。这个特定的状态估计问题是由应用领域中出现的问题引起的,这些问题处理的是结构相同的系统的种群,对于这些系统,只有在整体上才能测量种群,例如由于经济或技术原因。我们采用测量理论方法,其中群体由LTI系统建模,该系统描述了单个系统的结构和由离散度量表示的初始状态。我们导出了状态估计的特征,使其具有唯一解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the state estimation problem for discrete ensembles from discrete-time output snapshots
We consider the problem of reconstructing the initial states of a group of structurally identical LTI systems in the situation that output measurements of the individual systems in the group are received at discrete time steps and in an anonymized manner: While we do know all output measurements of the individual systems in the group, we do not know which output measurement corresponds to which system. This specific state estimation problem is motivated by emerging problems in applied fields that are dealing with populations of structurally identical systems for which it is only possible to measure the population as a whole, e.g. due to economic or technological reasons. We adopt a measure theoretical approach in which the group is modelled by an LTI system describing the structure of the individual systems and an initial state which is expressed by a discrete measure. We derive characterizations for the state estimation to admit a unique solution.
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