Extended space method for parameter identifiability of DAE systems.
Extended space method for parameter identifiability of DAE systems.
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DOI：
10.1016/j.isatra.2013.12.014
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发表时间：
2014-09
期刊：
影响因子：
7.3
通讯作者：
Li Chen;Xi Chen;Jixin Qian;Zhen Yao
中科院分区：
文献类型：
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作者：
Li Chen;Xi Chen;Jixin Qian;Zhen Yao
物理系统的数学模型通常具有必须从物理数据中识别的参数。这使得给定模型系统的参数可辨识性分析成为一个必要的先决条件。到目前为止，已经提出了几种方法来分析常微分方程（ODE）系统的参数可辨识性。但是，据我们所知，微分代数方程（DAE）系统的参数可辨识性很少被作为一个专门的课题进行分析。传统的微分代数（DA）方法通常直接应用于微分代数系统。然而，这些方法并不总是适用的，例如，当DAE系统不满足主要理想条件时。本文提出了一种新的方法来分析DAE系统的可辨识性，基于空间扩展的概念，通过代数和微分变量可以解耦。进而得到一个固有的、低维的、正则的常微分方程系统，它是原DAE系统的外等价。随后，微分代数（DA）方法，然后可以用来分析的低维常微分方程系统的可辨识性。理论分析也提出了所提出的方法。两个例子，包括一个简化的相互作用模型和等温反应器系统，给出了详细的步骤和所提出的方法的有效性。
Mathematical models of physical systems often have parameters that must be identified from physical data. This makes the analysis of the parameter identifiability of the given model system an essential prerequisite. Thus far, several methods have been proposed for analyzing the parameter identifiability of ordinary differential equation (ODE) systems. But, to the best of our knowledge, the parameter identifiability of differential algebraic equation (DAE) systems has scarcely been analyzed as a specific topic. Traditional differential algebraic (DA) methods developed for ODE systems are often applied directly on DAE systems. These methods, however, are not always applicable, e.g., when the prime ideal condition is not satisfied by a DAE system. In this paper, we propose a novel method to analyze the identifiability of DAE systems, based on the concept of space extension, through which the algebraic and differential variables can be decoupled. Furthermore, an inherent, low-dimensional, regular ODE system can be obtained, which is the external equivalent of the original DAE system. Subsequently, the differential algebraic (DA) method can then be used to analyze the identifiability of the low-dimension ODE system. Theoretical analysis is also presented for the proposed method. Two examples, including a simplified interaction model and an isothermal reactor system, are presented to illustrate the detailed steps and effectiveness of the proposed method.