A robust optimization approach to experimental design for model discrimination of dynamical systems

A high-ranking goal of interdisciplinary modeling approaches in science and engineering are quantitative prediction of system dynamics and model based optimization. Quantitative modeling has to be closely related to experimental investigations if the model is supposed to be used for mechanistic analysis and model predictions. Typically, before an appropriate model of an experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the models up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm which leads to the need for robustification. In this article we present a numerical algorithm which calculates a design of experiments allowing optimal discrimination of different hypothetic candidate models of a given dynamical system for the most inappropriate (worst case) parameter configurations within a parameter range. The design comprises initial values, system perturbations and the optimal placement of measurement time points, the number of measurements as well as the time points are subject to design. The statistical discrimination criterion is worked out rigorously for these settings, a derivation from the Kullback-Leibler divergence as optimization objective is presented for the case of discontinuous Heaviside-functions modeling the measurement decision which are replaced by continuous approximations during the optimization procedure. The resulting problem can be classified as a semi-infinite optimization problem which we solve in an outer approximations approach stabilized by a suggested homotopy strategy whose efficiency is demonstrated. We present the theoretical framework, algorithmic realization and numerical results.