### Abstract

Language | English |
---|---|

Title of host publication | Proceedings of the 17th IFAC World Congres |

Editors | Myung Yin Chung, Pradeep Misar |

Place of Publication | Seoul, Korea |

Pages | 313-318 |

Number of pages | 5 |

Volume | 41 |

DOIs | |

Publication status | Published - 2008 |

### Publication series

Name | IFAC Proceedings |
---|---|

Publisher | IFAC |

No. | 2 |

Volume | 41 |

### Fingerprint

### Keywords

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

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

AU - Fey, D.

AU - Findeisen, R.

AU - Bullinger, E.

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - parameter estimation

KW - parameter identi¯cation

KW - biological systems

KW - biochemical systems

KW - high-gain observers

KW - reduced-order observers

KW - observer Lyapunov function

UR - http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2008/start.htm

U2 - 10.3182/20080706-5-KR-1001.00053

DO - 10.3182/20080706-5-KR-1001.00053

M3 - Chapter

SN - 9783902661005

VL - 41

T3 - IFAC Proceedings

SP - 313

EP - 318

BT - Proceedings of the 17th IFAC World Congres

A2 - Chung, Myung Yin

A2 - Misar, Pradeep

CY - Seoul, Korea

ER -