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**Towards the identification of ordinary differential equations from measurements.**
*(English)*
Zbl 0665.34013

Special program on inverse problems, Proc. Cent. Math. Anal. Aust. Natl. Univ. 17, 60-79 (1988).

[For the entire collection see Zbl 0661.00013.]

The identification problem of estimating certain functions in a system of linear ordinary differential equations from measured data of its state is considered. The approach consists in an imbedding of the problem into a family of parameter-dependent problems which can be solved at least numerically. The corresponding solutions are proved to converge to the unknown functions as the parameters tend to infinity. Stability results with respect to disturbances in the measurements and the initial data are developed as well. The method is applied to determine mass exchange rates in a compartmental system of pharmaco-kinetic models.

The identification problem of estimating certain functions in a system of linear ordinary differential equations from measured data of its state is considered. The approach consists in an imbedding of the problem into a family of parameter-dependent problems which can be solved at least numerically. The corresponding solutions are proved to converge to the unknown functions as the parameters tend to infinity. Stability results with respect to disturbances in the measurements and the initial data are developed as well. The method is applied to determine mass exchange rates in a compartmental system of pharmaco-kinetic models.

### MSC:

34A55 | Inverse problems involving ordinary differential equations |

92Cxx | Physiological, cellular and medical topics |