Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems
Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems
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DOI：
10.1103/physrevx.9.041046
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发表时间：
2019-12-03
影响因子：
12.5
通讯作者：
Kschischo, Maik
中科院分区：
文献类型：
--
作者：
Kahl, Dominik;Wendland, Philipp;Kschischo, Maik
尽管我们对复杂动态网络的理解最近取得了进展，但在生物学、经济学或其他领域，设计足够精确的模型来观察、控制或预测真实系统的状态仍然具有挑战性。一个很大程度上被忽视的事实是，这些系统通常是开放的，并且接收来自其环境的未知输入。另一个根本障碍是由于对实际系统中定量相互作用的认识不足或不准确而引起的结构模型误差。在这里，我们表明开放系统的未知输入和模型误差可以在可逆性的通用框架下处理，这是从输出测量重建这些干扰的必要条件。利用系统的可逆性可以由系统的影响图决定的事实，分析了不同现实场景下结构网络性质与可逆性之间的关系。我们证明了稀疏连接的无标度网络是最难反转的。我们引入了一种新的传感器节点放置算法来选择网络中可逆性所需的最小测量位置集。该算法有助于从输出测量中重建输入或模型误差的最佳实验设计。我们的研究结果对非线性系统的分析、建模和设计具有基础和实际意义。
Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devise sufficiently accurate models to observe, control, or predict the state of real systems in biology, economics, or other fields. A largely overlooked fact is that these systems are typically open and receive unknown inputs from their environment. A further fundamental obstacle is structural model errors caused by insufficient or inaccurate knowledge about the quantitative interactions in the real system. Here, we show that unknown inputs to open systems and model errors can be treated under the common framework of invertibility, which is a requirement for reconstructing these disturbances from output measurements. By exploiting the fact that invertibility can be decided from the influence graph of the system, we analyze the relationship between structural network properties and invertibility under different realistic scenarios. We show that sparsely connected scale-free networks are the most difficult to invert. We introduce a new sensor node placement algorithm to select a minimum set of measurement positions in the network required for invertibility. This algorithm facilitates optimal experimental design for the reconstruction of inputs or model errors from output measurements. Our results have both fundamental and practical implications for nonlinear systems analysis, modeling, and design.