Influence of discretization errors on set-based parameter estimation

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.