Ensemble Observability of Linear Systems
Ensemble Observability of Linear Systems
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DOI：
10.1109/tac.2015.2463631
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发表时间：
2015-07
影响因子：
6.8
通讯作者：
Shen Zeng;S. Waldherr;C. Ebenbauer;F. Allgöwer
中科院分区：
文献类型：
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作者：
Shen Zeng;S. Waldherr;C. Ebenbauer;F. Allgöwer
我们讨论了用概率分布描述的系综的可观性问题。问题是在经典的有限维线性系统下，从输出概率分布的时间演化重建初始状态的概率分布。对于这个问题，我们提出了两种解决方案，一种是基于将问题描述为反问题，另一种是基于重构分布的所有矩。第一种方法将我们引向重建问题和数学层析成像问题之间的联系。在第二种方法中，我们使用张量系统的框架来描述力矩的动力学，这导致了对重建问题的更系统的理论处理。此外，我们还证明了这两个框架是内在相关的。有两个双重观点的吸引力，第一个是更几何的，第二个是更系统的理论，用几个具有理论或实践重要性的例子来说明。
We address the observability problem for ensembles that are described by probability distributions. The problem is to reconstruct a probability distribution of the initial state from the time-evolution of the probability distribution of the output under a classical finite-dimensional linear system. We present two solutions to this problem, one based on formulating the problem as an inverse problem and the other one based on reconstructing all the moments of the distribution. The first approach leads us to a connection between the reconstruction problem and mathematical tomography problems. In the second approach we use the framework of tensor systems to describe the dynamics of the moments, which leads to a more systems theoretic treatment of the reconstruction problem. Furthermore we show that both frameworks are inherently related. The appeal of having two dual viewpoints, the first being more geometric and the second one being more systems theoretic, is illuminated in several examples of theoretical or practical importance.