具有广义子系统的NDS的全局结构可识别性和可重构性
Global Structure Identifiability and Reconstructibility of an NDS with Descriptor Subsystems
摘要：
本文研究了网络化动态系统（NDS）的要求，使其子系统的相互作用可以单独从实验数据确定或从其整体模型重建。NDS是由几个子系统，其动态描述通过一个描述符形式。除了每个子系统和整个NDS的规律性，没有其他的限制，无论是子系统的动态或子系统之间的相互作用。基于矩阵秩，给出了子系统相互作用全局可辨识的充分必要条件，并由此得到了在存在先验信息时NDS结构可辨识的几个结论.该矩阵也给出了一个显式的描述子系统的相互作用，不能单独从实验数据区分。此外，在适定性假设下，得到了NDS描述子模型中子系统相互作用可重构的充分必要条件。这个条件可以验证与每个子系统分别，因此是有吸引力的分析和综合的大规模NDS。仿真结果表明，而不是单调增加的子系统相互作用的不可微集的距离，外部输出之间的差异与不同的子系统相互作用的两个NDS的幅度增加得更快，当其中一个是接近不稳定。此外，探测信号的方向对于区分不同的NDS的外部输出也是非常重要的，这些发现有望在识别实验设计等方面有所帮助。
英文摘要：
This paper investigates requirements on a networked dynamic system (NDS) such that its subsystem interactions can be solely determined from experiment data or reconstructed from its overall model. The NDS is constituted from several subsystems whose dynamics are described through a descriptor form. Except regularity on each subsystem and the whole NDS, no other restrictions are put on either subsystem dynamics or subsystem interactions. A matrix rank based necessary and sufficient condition is derived for the global identifiability of subsystem interactions, which leads to several conclusions about NDS structure identifiability when there is some a priori information. This matrix also gives an explicit description for the set of subsystem interactions that can not be distinguished from experiment data only. In addition, under a well-posedness assumption, a necessary and sufficient condition is obtained for the reconstructibility of subsystem interactions from an NDS descriptor form model. This condition can be verified with each subsystem separately and is therefore attractive in the analysis and synthesis of a large-scale NDS. Simulation results show that rather than increases monotonically with the distance of subsystem interactions to the undifferentiable set, the magnitude of the external output differences between two NDSs with distinct subsystem interactions increases much more rapidly when one of them is close to be unstable. In addition, directions of probing signals are also very important in distinguishing external outputs of distinctive NDSs.These findings are expected to be helpful in identification experiment designs, etc.
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