Similarity transformation approach to identifiability analysis of nonlinear compartmental models (Q911496)

The similarity transformation approach (exhaustive modeling) has been proposed by \textit{E. Walter} and \textit{Y. Lecourtier} [ibid. 56, 1-25 (1981; Zbl 0465.93028)] for the study of identifiability of linear models: the states of two controllable and observable linear systems having the same input-output map are related by a similarity transformation. If they correspond to the same system with two different values of the parameter to identify it will result in relations which can be used to prove global resp. local identifiability or unidentifiability of the system. In this paper, the method is extended to nonlinear systems. Using the tools of differential geometry, controllability and observability rank criteria can be defined [\textit{R. Hermann} and \textit{A. J. Krener}, IEEE Trans. Autom. Control AC-22, 728-740 (1977; Zbl 0396.93015)]. If they are satisfied, a local state isomorphism theorem, analogous to the similarity transformation in the linear case, can be used to derive necessary and sufficient conditions for global identifiability. Generally speaking, these include solving linear first order partial differential equations. In some cases, these conditions are much simpler and can be solved explicitly. They are used to give nontrivial examples of unidentifiable nonlinear systems and to study the identifiability of some compartmental models with Michaelis-Menten elimination kinetics which are of importance in pharmacokinetics. The method seems to be more tractable than the Taylor series expansion on these examples.