Vajda S, Godfrey K R, Rabitz H
Math Biosci. 1989 Apr;93(2):217-48. doi: 10.1016/0025-5564(89)90024-2.
Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.
通过使用局部状态同构定理而非线性系统理论的代数等价定理，相似变换方法被扩展到非线性模型，从而得出了全局和局部可识别性的有限可验证的充分必要条件。该方法需要测试某些可控性和可观测性条件，但在许多实际例子中，这些条件很容易验证。原则上，该方法也涉及非线性状态变量变换，但在本文给出的所有例子中，变换结果都是线性的。该方法被应用于一个不可识别的非线性模型和一个局部可识别的非线性模型，这是除双线性模型之外的首批非线性模型，其缺乏全局可识别性的原因并非微不足道。该方法还被应用于两个具有米氏消除动力学的模型，这两个模型在药代动力学中都相当重要，并且迄今为止，泰勒级数方法产生的代数方程的复杂性使得针对特定输入函数建立可识别性结果的尝试均告失败。
