Determination of Set-Membership Identifiability Sets

This paper concerns the concept of set-membership identifiability introduced in Jauberthie et al. (Proceedings of the 18th IFAC World Congress. Milan, Italie, 12024–12029, 2011). Given a model, a set-membership identifiable set is a connected set in the parameter domain of the model such that its corresponding trajectories are distinct to trajectories arising from its complementary. For obtaining the so-called set-membership identifiable sets, we propose an algorithm based on interval analysis tools. The proposed algorithm is decomposed into three parts namely mincing, evaluating and regularization (Jaulin et al. in Applied interval analysis, with examples in parameter and state estimation, robust control and robotics. Springer, Londres, 2001). The latter step has been modified in order to obtain guaranteed set-membership identifiable sets. Our algorithm will be tested on two examples.

[1]  Sebastien Lagrange,et al.  Injectivity analysis using interval analysis: Application to structural identifiability , 2008, Autom..

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

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

[4]  E. Walter,et al.  Estimation of parameter bounds from bounded-error data: a survey , 1990 .

[5]  Luc Jaulin,et al.  Contractor programming , 2009, Artif. Intell..

[6]  Eric Walter,et al.  Guaranteed numerical alternatives to structural identifiability testing , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[8]  Carine Jauberthie,et al.  Fault detection and identification relying on set-membership identifiability , 2013, Annu. Rev. Control..

[9]  E. Walter,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2001 .

[10]  Antonio Vicino,et al.  Estimation theory for nonlinear models and set membership uncertainty , 1991, Autom..

[11]  Luc Jaulin,et al.  Applied Interval Analysis , 2001, Springer London.

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

[13]  Carine Jauberthie,et al.  Set-membership identifiability: definitions and analysis , 2011 .

[14]  James R. Munkres,et al.  Topology; a first course , 1974 .

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

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

[17]  Carine Jauberthie,et al.  Fault Detection and Identification relying on set-membership Identifiability , 2012 .

[18]  Carine Jauberthie,et al.  Set-membership identifiability of nonlinear models and related parameter estimation properties , 2016, Int. J. Appl. Math. Comput. Sci..

[19]  J. Norton,et al.  Bounding Approaches to System Identification , 1996 .