论文标题
具有LFT结构的描述符系统的频域可识别性和滑坡
Frequency Domain Identifiability and Sloppiness of Descriptor Systems with an LFT Structure
论文作者
论文摘要
在本文中，根据其频率响应样本研究了描述符系统的参数。建议分别提出两个指标，以测量参数矢量的绝对性和相对斜率。在此描述符系统中，假定系统矩阵通过线性分数转换（LFT）取决于其参数。当关联的传输函数矩阵（TFM）具有完整的正常行等级时，基于矩阵等级的必要条件和足够的条件是针对参数可识别性的，并有一组有限的频率响应。可以递归地验证这种情况，这在计算上非常吸引人，尤其是当系统大规模时。从这种情况下，建议一种算法找到一组频率，该频率能够与系统的频率响应能够唯一确定其参数。给出了由所有参数值组成的集合的椭圆形近似，相关描述符系统具有频率响应，该频率响应在规定的距离内偏离与与全球可识别的参数矢量值相对应的偏差。也为建议的绝对和相对滑坡指标得出了显式公式。
Identifiability and sloppiness are investigated in this paper for the parameters of a descriptor system based on its frequency response samples. Two metrics are suggested respectively for measuring absolute and relative sloppiness of the parameter vector at a prescribed value. In this descriptor system, system matrices are assumed to depend on its parameters through a linear fractional transformation (LFT). When an associated transfer function matrix (TFM) is of full normal row rank, a matrix rank based necessary and sufficient condition is derived for parameter identifiability with a set of finitely many frequency responses. This condition can be verified recursively which is computationally quite appealing, especially when the system is of a large scale. From this condition, an algorithm is suggested to find a set of frequencies with which the frequency responses of the system are capable to uniquely determine its parameters. An ellipsoid approximation is given for the set consisting of all the parameter values with which the associated descriptor system has a frequency response that deviates within a prescribed distance, from that corresponding to a globally identifiable parameter vector value. Explicit formulas are also derived for the suggested absolute and relative sloppiness metrics.
