Set-membership identifiability: definitions and analysis

Abstract Definitions and methods for checking the identifiability of linear and nonlinear systems are now well established. However this property has not really been investigated for uncertain systems, in particular for set-membership models in a bounded-error context. In this paper, we propose two complementary definitions, set-membership identifiability and μ-set-membership identifiability, the first one is conceptual whereas the second can be put in correspondence with existing set-membership parameter estimation methods. The links between these definitions are exhibited and two methods to check the properties are proposed, illustrated by examples.

[1]  Claudio Cobelli,et al.  Global identifiability of nonlinear models of biological systems , 2001, IEEE Transactions on Biomedical Engineering.

[2]  Lilianne Denis-Vidal,et al.  Some remarks about identifiability of controlled and uncontrolled nonlinear systems , 1997, 1997 European Control Conference (ECC).

[3]  Ghislaine Joly-Blanchard,et al.  Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor , 2005 .

[4]  Y. Candau,et al.  Set membership state and parameter estimation for systems described by nonlinear differential equations , 2004, Autom..

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

[6]  Carine Jauberthie,et al.  State estimation by interval analysis for a nonlinear differential aerospace model , 2007, 2007 European Control Conference (ECC).

[7]  Michel Petitot,et al.  An Algorithm to Test Identifiability of Non-Linear Systems , 2001 .

[8]  Eric Walter,et al.  Set inversion via interval analysis for nonlinear bounded-error estimation , 1993, Autom..

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

[10]  E. Walter,et al.  Interval Analysis for Guaranteed Nonlinear Parameter Estimation , 2003 .

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

[12]  Eric Walter,et al.  Guaranteed recursive non‐linear state bounding using interval analysis , 2002 .

[13]  Alex M. Andrew,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2002 .

[14]  Vicenç Puig,et al.  ROBUST FAULT DETECTION WITH UNKNOWN INPUT SET-MEMBERSHIP STATE ESTIMATORS AND INTERVAL MODELS USING ZONOTOPES , 2006 .

[15]  Ghislaine Joly-Blanchard,et al.  Some Remarks about an Identifiability Result of Nonlinear Systems , 1998, Autom..

[16]  Josep Vehí,et al.  A Survey on Interval Model Simulators and their Properties Related to Fault Detection , 2000 .

[17]  Eva Riccomagno,et al.  Structural identifiability analysis of some highly structured families of statespace models using differential algebra , 2004, Journal of mathematical biology.

[18]  J J Distefano,et al.  Parameter space boundaries for unidentifiable compartmental models. , 1989, Mathematical biosciences.

[19]  E. Kolchin.  Differential Algebra and Algebraic Groups , 2012 .

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

[21]  E. Walter,et al.  Global approaches to identifiability testing for linear and nonlinear state space models , 1982 .

[22]  Sebastien Lagrange,et al.  On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis , 2007, Reliab. Comput..

[23]  Josep Vehí,et al.  Application of Modal Intervals to the Generation of Error-Bounded Envelopes , 2001, Reliab. Comput..

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

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

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

[27]  Keith R. Godfrey,et al.  Structural identifiability of non-linear systems using linear/non-linear splitting , 2003 .

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

[29]  Nicolas Bourbaki,et al.  Elements of mathematics , 2004 .

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