Influence of discretization errors on set-based parameter estimation

P. Rumschinski, Dina Shona Laila, S. Borchers, R. Findeisen

Research output: Contribution to conferencePaper

6 Citations (Scopus)

Abstract

In this paper we investigate the relationship between parameter estimates obtained for a nonlinear discrete-time (DT) approximation of a continuous-time (CT) nonlinear model and the parameters corresponding to the CT model itself. Preliminary results based on a set-based parameter estimation approach are proposed. The focus is thereby directed on formalizing the problem of ensuring that the set of consistent parameters of the CT model are also related to the consistent parameters of the DT model. Therefore, we propose two approaches to handle this problem. The first is based on a direct treatment of the discretization error, while the other is based on a differential geometric relationship of Euler discretization and the CT model. Two examples, one academic example and another one applying the proposed results to a well-known biological process, namely the Michaelis-Menten (MM) reaction, are presented to illustrate the usefulness of the results.
Original languageEnglish
Pages296-301
DOIs
Publication statusPublished - 22 Feb 2011
EventIEEE Conference on Decision and Control - Georgia, Atlanta, United States
Duration: 15 Dec 201017 Dec 2010

Conference

ConferenceIEEE Conference on Decision and Control
CountryUnited States
CityAtlanta
Period15/12/1017/12/10

Fingerprint

Continuous-time Model
Discretization Error
Parameter Estimation
Discrete-time Model
Nonlinear Model
Euler
Discrete-time
Discretization
Influence
Approximation
Estimate
Relationships

Bibliographical note

The full text is currently unavailable on the repository.

Keywords

  • Mathematical model
  • Biological system modeling
  • Data models
  • Numerical models
  • Lead
  • Parameter estimation
  • Approximation methods
  • parameter estimation
  • approximation theory
  • discrete time systems
  • nonlinear control systems
  • Michaelis-Menten reaction
  • discretization errors
  • set based parameter estimation
  • nonlinear discrete-time approximation
  • continuous-time nonlinear model
  • set-based parameter estimation
  • direct treatment
  • differential geometric relationship
  • Euler discretization
  • CT model
  • biological process

Cite this

Rumschinski, P., Laila, D. S., Borchers, S., & Findeisen, R. (2011). Influence of discretization errors on set-based parameter estimation. 296-301. Paper presented at IEEE Conference on Decision and Control, Atlanta, United States. https://doi.org/10.1109/CDC.2010.5717519

Influence of discretization errors on set-based parameter estimation. / Rumschinski, P.; Laila, Dina Shona; Borchers, S.; Findeisen, R.

2011. 296-301 Paper presented at IEEE Conference on Decision and Control, Atlanta, United States.

Research output: Contribution to conferencePaper

Rumschinski, P, Laila, DS, Borchers, S & Findeisen, R 2011, 'Influence of discretization errors on set-based parameter estimation' Paper presented at IEEE Conference on Decision and Control, Atlanta, United States, 15/12/10 - 17/12/10, pp. 296-301. https://doi.org/10.1109/CDC.2010.5717519
Rumschinski P, Laila DS, Borchers S, Findeisen R. Influence of discretization errors on set-based parameter estimation. 2011. Paper presented at IEEE Conference on Decision and Control, Atlanta, United States. https://doi.org/10.1109/CDC.2010.5717519
Rumschinski, P. ; Laila, Dina Shona ; Borchers, S. ; Findeisen, R. / Influence of discretization errors on set-based parameter estimation. Paper presented at IEEE Conference on Decision and Control, Atlanta, United States.
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