Identifiability of Linear and Linear-in-Parameters Dynamical Systems from a Single Trajectory
Identifiability of Linear and Linear-in-Parameters Dynamical Systems from a Single Trajectory
复制标题
DOI：
10.1137/130937913
复制
发表时间：
2014-01-01
影响因子：
2.1
通讯作者：
Swigon, D.
中科院分区：
文献类型：
--
作者：
Stanhope, S.;Rubin, J. E.;Swigon, D.
某些实验是不可重复的，因为它们导致被研究系统的破坏或改变，从而提供了在状态空间中最多包含单一轨迹的数据。在继续对这类系统的模型进行参数估计之前，重要的是知道是否可以从理想化(无误差)的单轨数据中唯一地确定或识别模型参数。在线性模型的情况下，我们给出了几种形式的可辨识性的精确定义，并导出了一些新的、相互关联的条件，这些条件是这些形式可辨识性出现的充要条件。我们还证明了这些结果直接推广到一类参数为线性的非线性系统。我们的一个结果提供了关于可辨识性的信息，仅基于观察到的轨迹的几何结构，而其他结果与是否存在初始条件有关，该初始条件产生固定的但未知的系数矩阵的可辨识性，并取决于其Jordan结构或其他性质。最后，我们将可辨识性与Jordan结构之间的关系推广到离散数据的情形，并证明了离散数据参数估计的灵敏度依赖于与数据的空间限制有关的条件数。
Certain experiments are nonrepeatable because they result in the destruction or alteration of the system under study, and thus provide data consisting of at most a single trajectory in state space. Before proceeding with parameter estimation for models of such systems, it is important to know whether the model parameters can be uniquely determined, or identified, from idealized (error-free) single trajectory data. In the case of a linear model, we provide precise definitions of several forms of identifiability, and we derive some novel, interrelated conditions that are necessary and sufficient for these forms of identifiability to arise. We also show that the results have a direct extension to a class of nonlinear systems that are linear in parameters. One of our results provides information about identifiability based solely on the geometric structure of an observed trajectory, while other results relate to whether or not there exists an initial condition that yields identifiability of a fixed but unknown coefficient matrix and depend on its Jordan structure or other properties. Lastly, we extend the relation between identifiability and Jordan structure to the case of discrete data, and we show that the sensitivity of parameter estimation with discrete data depends on a condition number related to the data's spatial confinement.