论文标题
具有LFT参数化子系统的ND的结构可识别性
Structure Identifiability of an NDS with LFT Parametrized Subsystems
论文作者
论文摘要
在本文中，对子系统的要求已经明确了线性时间不变（LTI）网络动态系统（NDS），根据该系统，可以从外部输出测量值中估算子系统互连。在此NDS中，子系统可能具有独特的动态，并且子系统互连是任意的。假定每个子系统的系统矩阵取决于其（伪）的第一个原理参数（FPP），这是通过线性分数转换（LFT）。已经证明，如果在每个子系统中，传输函数矩阵（TFM）从其内部输入到其外部输出为完整的正常列等级（FNCR），而TFM从外部输入到其内部输出为完整的正常行等级（FNRR），则NDS的结构是可识别的。此外，在某些特定情况下，例如从内部输入到每个子系统中的内部输出没有直接的信息传输，为NDS结构可识别建立了必要和足够的条件。基于矩阵值的多项式（MVP）等效条件得到了进一步得出，这取决于子系统（伪）FPP，并且可以独立验证每个子系统。从这种情况下，使用矩阵铅笔的Kronecker规范形式（KCF）获得了子系统动力学及其（伪）FPP的一些必要条件。
Requirements on subsystems have been made clear in this paper for a linear time invariant (LTI) networked dynamic system (NDS), under which subsystem interconnections can be estimated from external output measurements. In this NDS, subsystems may have distinctive dynamics, and subsystem interconnections are arbitrary. It is assumed that system matrices of each subsystem depend on its (pseudo) first principle parameters (FPPs) through a linear fractional transformation (LFT). It has been proven that if in each subsystem, the transfer function matrix (TFM) from its internal inputs to its external outputs is of full normal column rank (FNCR), while the TFM from its external inputs to its internal outputs is of full normal row rank (FNRR), then the structure of the NDS is identifiable. Moreover, under some particular situations like there are no direct information transmission from an internal input to an internal output in each subsystem, a necessary and sufficient condition is established for NDS structure identifiability. A matrix valued polynomial (MVP) rank based equivalent condition is further derived, which depends affinely on subsystem (pseudo) FPPs and can be independently verified for each subsystem. From this condition, some necessary conditions are obtained for both subsystem dynamics and its (pseudo) FPPs, using the Kronecker canonical form (KCF) of a matrix pencil.
