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首页> 外文期刊>Physical Review X >Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems
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Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

机译：动态系统中的误差和输入重建的结构可动性和最佳传感器节点放置

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摘要

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.
机译：尽管最近对我们对复杂的动态网络的理解进行了进展，但设计了足够准确的模型来观察，控制或预测生物学，经济学或其他领域的真实系统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打开的，并从其环境中接收未知的输入。另一个基本障碍是由真实系统中定量相互作用的知识不足或不准确的结构模型错误。在这里，我们显示未知系统和模型错误的未知输入可以在可逆性框架下处理，这是从输出测量重建这些干扰的要求。通过利用可以从系统的影响图中决定可逆性的事实，我们在不同现实场景下分析了结构网络性质与可逆性之间的关系。我们表明，稀疏连接的无垢网络是最难以反转的。我们介绍了一种新的传感器节点放置算法，可在可逆性所需的网络中选择最小的测量位置。该算法有助于从输出测量重建输入或模型误差的最佳实验设计。我们的结果对非线性系统分析，建模和设计具有基本和实际的影响。

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