The Library

Structural identifiability analysis via symmetries of differential equations

Tools

Yates, James W. T., Evans, N. D. and Chappell, M. J. (Michael J.). (2009) Structural identifiability analysis via symmetries of differential equations. Automatica, Vol.45 (No.11). pp. 2585-2591. ISSN 0005-1098

Preview

PDF
WRAP_Evans_9871863-es-121211-symmetry_final.pdf - Accepted Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (287Kb)

Official URL: http://dx.doi.org/10.1016/j.automatica.2009.07.009

Abstract

Results and derivations are presented for the generation of a local Lie algebra that represents the 'symmetries' of a set of coupled differential equations. The subalgebra preserving the observation defined on the model structure is found, thus giving all transformations of the system that preserve its structure. It is shown that this is equivalent to the similarity transformation approach (Evans, Chapman, Chappell, & Godfrey, 2002) for structural identifiability analysis and as such is a method of generating such transformations for this approach. This provides another method for performing structural identifiability analysis on nonlinear state-space models that has the possibility of extension to PDE type models. The analysis is easily automated and performed in MATHEMATICA, and this is demonstrated by application the technique to a number of practical examples from the literature.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General)
Divisions:	Faculty of Science > Engineering
Library of Congress Subject Headings (LCSH):	Differential equations , Parameter estimation, Lie algebras
Journal or Publication Title:	Automatica
Publisher:	Pergamon
ISSN:	0005-1098
Date:	November 2009
Volume:	Vol.45
Number:	No.11
Number of Pages:	7
Page Range:	pp. 2585-2591
Identification Number:	10.1016/j.automatica.2009.07.009
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
References:	[1] N.D. Evans, M.J. Chapman, M.J. Chappell, and K.R. Godfrey. Identi�ability of uncontrolled nonlinear rational systems. Automatica, 3:1799{1805, 2002. [2] G. Margaria, E. Riccomagno, M.J. Chappell, and H.P. Wynn. Di�erential algebra methods for the study of the structural identi�ability of rational function state-space models in the biosciences. Mathematical Biosciences, 174:1{26, 2001. [3] G. Margaria, E. Riccomagno, and L.J. White. Structural identi�ability analysis of some highly structured families of statespace models using di�erential algebra. Journal of Mathematical Biology, 49:433{454, 2004. [4] M.P. Saccomani, S. Audoly, and L. D'Angio. Parameter identi�ability of nonlinear systems: the role of initial conditions. Automatica, 39:619{632, 2003. [5] The Mathematica Book. Wolfram Media Inc,US, 2004. [6] R.A. Nicolaides and N.J. Walkington. Maple: A Comprehensive Introduction. Cambridge University Press, 1996. [7] P.J. Olver. Applications of Lie Groups to Di�erential Equations. Springer, London, second edition edition, 2000. [8] P.L. Sachdev. Self-similarity and Beyond: Exact Solutions of Nonlinear Problems. Chapman and Hall/CRC, Boca Raton, 2000. [9] L. Ljung and T. Glad. On global identi�ability for arbitrary model parametrizations. Automatica, 30(2):265{278, 1994. [10] A. Sedoglavic. A probabilistic algorithm to test local algebraic observability in polynomial time. Journal of Symbolic Computation, 33(5):735{755, 2002. [11] D. Cox, J. Little, and D. O'Shea. Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, London, second edition edition, 1997. [12] B.J. Cantwell. Introduction to Symmetry Analysis (Cambridge Texts in Applied Mathematics). Cambridge University Press, Cambridge, UK, 2002. [13] L. Denis-Vidal and G. Joly-Blanchard. Equivalence and identi�ability analysis on uncontrolled nonlinear dynamical systems. Automatica, 40:287{292, 2004. [14] K.R. Godfrey. Compartmental Models and their application. Academic Press, Inc. London., 1983.
URI:	http://wrap.warwick.ac.uk/id/eprint/16955