Towards the identification of ordinary differential equations from measurements

Abstract

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 measmements and the initial data are developed as welL The method is applied to detennine mass exchange rates in a compartmental system of pharmaco--kinetic models.