### Abstract

This paper sets forth and illustrates some techniques for parameter identification (PId) of a nonlinear state model that approximates the dynamical behavior of the humoral immune response of a human to Haemophilus influenzae Type-b. The natural physiological time-separation of the primary, late follicular, and secondary immune responses of this biological process allows us to divide the PId problem into a sequence of smaller PId sub-problems. To reduce the dimension of the PId even further, coupling effects are minimized or eliminated by temporarily replacing variables and/or certain other functions of variables by approximate a priori known time functions called exogenous inputs. This sequence of low dimensional PId problems entails matching a set of one or two parameters at each step to a time-attribute pair defined as a maximum or minimum measured concentration level in a given time window. The identification sub-problem solution reduces to the inverse of an approximate local parameter-to-measurement map. The techniques presented herein are applicable to other nonlinear systems which exhibit similar time-sequenced properties.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 1998 American Control Conference, ACC 1998 |

Pages | 3585-3589 |

Number of pages | 5 |

Volume | 6 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | 1998 American Control Conference, ACC 1998 - Philadelphia, PA, United States Duration: Jun 24 1998 → Jun 26 1998 |

### Other

Other | 1998 American Control Conference, ACC 1998 |
---|---|

Country | United States |

City | Philadelphia, PA |

Period | 6/24/98 → 6/26/98 |

### Fingerprint

### Keywords

- Biological process
- Humoral immune response
- Identification
- Nonlinear model
- Simulation

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 1998 American Control Conference, ACC 1998*(Vol. 6, pp. 3585-3589). [703280] https://doi.org/10.1109/ACC.1998.703280

**Parameter identification for an autonomous 11th order nonlinear model of a physiological process.** / Rundell, A.; DeCarlo, R.; Doerschuk, P.; HogenEsch, Harm.

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

*Proceedings of the 1998 American Control Conference, ACC 1998.*vol. 6, 703280, pp. 3585-3589, 1998 American Control Conference, ACC 1998, Philadelphia, PA, United States, 6/24/98. https://doi.org/10.1109/ACC.1998.703280

}

TY - GEN

T1 - Parameter identification for an autonomous 11th order nonlinear model of a physiological process

AU - Rundell, A.

AU - DeCarlo, R.

AU - Doerschuk, P.

AU - HogenEsch, Harm

PY - 1998

Y1 - 1998

N2 - This paper sets forth and illustrates some techniques for parameter identification (PId) of a nonlinear state model that approximates the dynamical behavior of the humoral immune response of a human to Haemophilus influenzae Type-b. The natural physiological time-separation of the primary, late follicular, and secondary immune responses of this biological process allows us to divide the PId problem into a sequence of smaller PId sub-problems. To reduce the dimension of the PId even further, coupling effects are minimized or eliminated by temporarily replacing variables and/or certain other functions of variables by approximate a priori known time functions called exogenous inputs. This sequence of low dimensional PId problems entails matching a set of one or two parameters at each step to a time-attribute pair defined as a maximum or minimum measured concentration level in a given time window. The identification sub-problem solution reduces to the inverse of an approximate local parameter-to-measurement map. The techniques presented herein are applicable to other nonlinear systems which exhibit similar time-sequenced properties.

AB - This paper sets forth and illustrates some techniques for parameter identification (PId) of a nonlinear state model that approximates the dynamical behavior of the humoral immune response of a human to Haemophilus influenzae Type-b. The natural physiological time-separation of the primary, late follicular, and secondary immune responses of this biological process allows us to divide the PId problem into a sequence of smaller PId sub-problems. To reduce the dimension of the PId even further, coupling effects are minimized or eliminated by temporarily replacing variables and/or certain other functions of variables by approximate a priori known time functions called exogenous inputs. This sequence of low dimensional PId problems entails matching a set of one or two parameters at each step to a time-attribute pair defined as a maximum or minimum measured concentration level in a given time window. The identification sub-problem solution reduces to the inverse of an approximate local parameter-to-measurement map. The techniques presented herein are applicable to other nonlinear systems which exhibit similar time-sequenced properties.

KW - Biological process

KW - Humoral immune response

KW - Identification

KW - Nonlinear model

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=35048900203&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35048900203&partnerID=8YFLogxK

U2 - 10.1109/ACC.1998.703280

DO - 10.1109/ACC.1998.703280

M3 - Conference contribution

SN - 0780345304

SN - 9780780345300

VL - 6

SP - 3585

EP - 3589

BT - Proceedings of the 1998 American Control Conference, ACC 1998

ER -