Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

D. Fey, R. Findeisen, E. Bullinger

Research output: Chapter in Book/Report/Conference proceedingChapter

15 Citations (Scopus)

Abstract

An essential part of mathematical modelling is the accurate and reliable estimation of model parameters. In biology, the required parameters are particularly difficult to measure due to either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, resulting from generalised mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using suitable nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables. An important advantage of the proposed method is that it allows to identify suitable measurements and/or model structures for which the parameters can be estimated. Furthermore, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation.
LanguageEnglish
Title of host publicationProceedings of the 17th IFAC World Congres
EditorsMyung Yin Chung, Pradeep Misar
Place of PublicationSeoul, Korea
Pages313-318
Number of pages5
Volume41
DOIs
Publication statusPublished - 2008

Publication series

NameIFAC Proceedings
PublisherIFAC
No.2
Volume41

Fingerprint

reaction kinetics
biology
bionics
gene expression
differential equations
nonlinearity
kinetics
estimates
products

Keywords

  • parameter estimation
  • parameter identi¯cation
  • biological systems
  • biochemical systems
  • high-gain observers
  • reduced-order observers
  • observer Lyapunov function

Cite this

Fey, D., Findeisen, R., & Bullinger, E. (2008). Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions. In M. Y. Chung, & P. Misar (Eds.), Proceedings of the 17th IFAC World Congres (Vol. 41, pp. 313-318). (IFAC Proceedings; Vol. 41, No. 2). Seoul, Korea. https://doi.org/10.3182/20080706-5-KR-1001.00053
Fey, D. ; Findeisen, R. ; Bullinger, E. / Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions. Proceedings of the 17th IFAC World Congres. editor / Myung Yin Chung ; Pradeep Misar. Vol. 41 Seoul, Korea, 2008. pp. 313-318 (IFAC Proceedings; 2).
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Fey, D, Findeisen, R & Bullinger, E 2008, Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions. in MY Chung & P Misar (eds), Proceedings of the 17th IFAC World Congres. vol. 41, IFAC Proceedings, no. 2, vol. 41, Seoul, Korea, pp. 313-318. https://doi.org/10.3182/20080706-5-KR-1001.00053

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions. / Fey, D.; Findeisen, R.; Bullinger, E.

Proceedings of the 17th IFAC World Congres. ed. / Myung Yin Chung; Pradeep Misar. Vol. 41 Seoul, Korea, 2008. p. 313-318 (IFAC Proceedings; Vol. 41, No. 2).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Fey D, Findeisen R, Bullinger E. Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions. In Chung MY, Misar P, editors, Proceedings of the 17th IFAC World Congres. Vol. 41. Seoul, Korea. 2008. p. 313-318. (IFAC Proceedings; 2). https://doi.org/10.3182/20080706-5-KR-1001.00053