Extensions to a procedure for generating locally identifiable reparameterisations of unidentifiable systems.

In this paper extensions to an existing procedure for generating locally identifiable reparameterisations of unidentifiable systems are presented. These extensions further formalise the constructive nature of the methodology and lend themselves to application within symbolic manipulation packages. The extended reparameterisation procedure is described in detail and is illustrated with application to two known non-trivial examples of unidentifiable systems of practical relevance.

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

[2]  S. Vajda,et al.  IDENTIFIABILITY OF POLYNOMIAL SYSTEMS: STRUCTURAL AND NUMERICAL ASPECTS , 1987 .

[3]  T. Rothenberg.  Identification in Parametric Models , 1971 .

[4]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

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

[6]  Eric Walter,et al.  Identifiability of parametric models , 1987 .

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

[8]  A. Isidori.  Nonlinear Control Systems , 1985 .

[9]  Joseph J. DiStefano,et al.  Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems , 1983 .

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

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

[12]  A. Holmberg.  On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities , 1982 .

[13]  K. R. Godfrey,et al.  Identifiability and indistinguishability of linear compartmental models , 1990 .

[14]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[15]  Keith R. Godfrey,et al.  Structural identifiability of controlled state space systems: a quasiautomated methodology for generating identifiable reparameterisations of unidentifiable systems , 1999 .

[16]  Claudio Cobelli,et al.  Theoretical Aspects and Practical Strategies for the Identification of Unidentifiable Compartmental Systems , 1985 .

[17]  M. Milanese,et al.  Decomposition methods for the identifiability analysis of large systemsy , 1978 .

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

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

[20]  K R Godfrey,et al.  Indistinguishability for a class of nonlinear compartmental models. , 1994, Mathematical biosciences.

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

[22]  R N Gunn,et al.  A procedure for generating locally identifiable reparameterisations of unidentifiable non-linear systems by the similarity transformation approach. , 1998, Mathematical biosciences.

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

[24]  S. Vajda,et al.  Structural Identifiability of Linear, Bilinear, Polynomial and Rational Systems , 1984 .

[25]  G. Toffolo,et al.  Chapter 8 – THEORETICAL ASPECTS AND PRACTICAL STRATEGIES FOR THE IDENTIFICATION OF UNIDENTIFIABLE COMPARTMENTAL SYSTEMS , 1987 .

[26]  Roger N. Gunn,et al.  Reparameterisation of Unidentifiable Systems using the Taylor Series Approach , 1997 .

[27]  Stephen Wolfram,et al.  The Mathematica book (3rd ed.) , 1996 .