Identifiability of discrete-time nonlinear systems: The local state isomorphism approach

A new theorem is provided to test the identifiability of discrete-time systems with polynomial nonlinearities. That extends to discrete-time systems the local state isomorphism approach for continuous-time systems. Two examples are provided to illustrate the approach.

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

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

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

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

[5]  Gérard Bloch,et al.  Chaotic Cryptosystems: Cryptanalysis and Identifiability , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Dongming Wang Elimination Theory, Methods, and Practice , 2001 .

[7]  Eduardo Sontag Polynomial Response Maps , 1979 .

[8]  Maria Pia Saccomani,et al.  Parameter identifiability of nonlinear systems: the role of initial conditions , 2003, Autom..

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

[10]  C. Moog,et al.  Identifiability of discrete-time nonlinear systems , 2004 .

[11]  Eric Walter,et al.  On the identifiability and distinguishability of nonlinear parametric models , 1996 .

[12]  Ghislaine Joly-Blanchard,et al.  Some effective approaches to check the identifiability of uncontrolled nonlinear systems , 2001 .

[13]  M. Fliess,et al.  Nonlinear observability, identifiability, and persistent trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

[15]  Bruno Buchberger,et al.  Bruno Buchberger's PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal , 2006, J. Symb. Comput..

[16]  Ghislaine Joly-Blanchard,et al.  System Identifiability (Symbolic Computation) and Parameter Estimation (Numerical Computation) , 2003, Numerical Algorithms.

[17]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .