Parameter identifiability of nonlinear systems:: the role of initial conditions
Parameter identifiability of nonlinear systems:: the role of initial conditions
复制标题
DOI：
10.1016/s0005-1098(02)00302-3
复制
发表时间：
2003-04-01
期刊：
影响因子：
6.4
通讯作者：
D'Angiò, L
中科院分区：
文献类型：
--
作者：
Saccomani, MP;Audoly, S;D'Angiò, L
可辨识性是模型辨识的基本前提;它涉及在无噪声观测和无误差模型结构的理想条件下，从输入-输出数据确定的模型参数的唯一性。在20世纪80年代后期，微分代数的概念被引入控制和系统理论。近年来，微分代数工具已被应用于研究由多项式方程描述的动态系统的可辨识性。这些方法都利用了定义系统的多项式所产生的微分理想的特征集。在本文中，它将被证明，可识别性测试程序的基础上微分代数可能会失败的系统是在特定的初始条件开始，这个问题是严格相关的系统从给定的初始条件的可访问性。特别是，当系统不能从给定的初始条件下访问时，具有定义动态系统的多项式作为生成元的理想I可能不能正确地描述解的流形。在这种情况下，一个新的理想，包括所有的微分多项式消失的动力系统的解决方案，从初始条件开始，应计算。提出了一种可识别性检验，在一定的技术假设下，也适用于具有特定初始条件的系统。(C)2003爱思唯尔科技有限公司版权所有。
Identifiability is a fundamental prerequisite for model identification; it concerns uniqueness of the model parameters determined from the input-output data, under ideal conditions of noise-free observations and error-free model structure. In the late 1980s concepts of differential algebra have been introduced in control and system theory. Recently, differential algebra tools have been applied to study the identifiability of dynamic systems described by polynomial equations. These methods all exploit the characteristic set of the differential ideal generated by the polynomials defining the system. In this paper, it will be shown that the identifiability test procedures based on differential algebra may fail for systems which are started at specific initial conditions and that this problem is strictly related to the accessibility of the system from the given initial conditions. In particular, when the system is not accessible from the given initial conditions, the ideal I having as generators the polynomials defining the dynamic system may not correctly describe the manifold of the solution. In this case a new ideal that includes all differential polynomials vanishing at the solution of the dynamic system started from the initial conditions should be calculated. An identifiability test is proposed which works, under certain technical hypothesis, also for systems with specific initial conditions. (C) 2003 Elsevier Science Ltd. All rights reserved.