Structural identifiability of non-linear systems using linear/non-linear splitting

In this paper, the local state space isomorphism theorem for non-linear systems is used to analyse structural identifiability. In particular it is shown that, under certain restrictions, it is possible to perform a linear/non-linear splitting of the analysis. The relatively straightforward linear analysis then restricts the class of local diffeomorphic transformations as given by the non-linear state space isomorphism theorem. This, in turn, leads to possible simplifications to the subsequent non-linear analysis by providing an efficient means for calculating the local state diffeomorphism.

[1]  Héctor J. Sussmann,et al.  Existence and uniqueness of minimal realizations of nonlinear systems , 1976, Mathematical systems theory.

[2]  H. Rabitz,et al.  State isomorphism approach to global identifiability of nonlinear systems , 1989 .

[3]  A. van Peer,et al.  A Model with Separate Hepato-Portal Compartment ("First-Pass" Model): Fitting to Plasma Concentration-Time Profiles in Humans , 1997, Pharmaceutical Research.

[4]  K R Godfrey,et al.  Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. , 1990, Mathematical biosciences.

[5]  J. Wagner,et al.  A nonlinear physiologic pharmacokinetic model: I. Steady-state , 1985, Journal of Pharmacokinetics and Biopharmaceutics.

[6]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[7]  Keith R. Godfrey,et al.  Identifiability of uncontrolled nonlinear rational systems , 2002, Autom..

[8]  Keith R. Godfrey,et al.  Nonlinear compartmental model indistinguishability , 1996, Autom..

[9]  André Heck,et al.  Introduction to Maple , 1993 .

[10]  Yves Lecourtier,et al.  Unidentifiable compartmental models: what to do? , 1981 .

[11]  T. Tarn,et al.  New results for identifiability of nonlinear systems , 1987 .

[12]  J. DiStefano,et al.  Identifiability of Model Parameter , 1985 .

[13]  H. Rabitz,et al.  Similarity transformation approach to identifiability analysis of nonlinear compartmental models. , 1989, Mathematical biosciences.

[14]  A. Krener,et al.  Nonlinear controllability and observability , 1977 .

[15]  K R Godfrey,et al.  Structural identifiability of the parameters of a nonlinear batch reactor model. , 1992, Mathematical biosciences.

[16]  K. R. Godfrey,et al.  Chapter 1 – IDENTIFIABILITY OF MODEL PARAMETERS , 1987 .

[17]  Arild Thowsen,et al.  Structural identifiability , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[18]  Eric Walter,et al.  Identifiability of State Space Models , 1982 .