Experimental design tools for ordinary and algebraic differential equations

The purpose of this paper is to present practical tools to facilitate the interpretation of parameter estimation results and to optimize experimental designs, where the underlying dynamical model consists of systems of ordinary or algebraic differential equations. We present a heuristic procedure to compute significance levels of model parameters and allow successive elimination of redundant ones. To compute the optimal experimental designs, we choose the A-criterion to evaluate the performance of the system, i.e., the identifiability of model parameters to be computed after getting the experimental data. Pseudo-weights are introduced and treated as design variables, to reduce the number of experiments and determine those time values at which experiments should be taken. A couple of practically relevant case studies from chemical engineering are included, which have been investigated previously by other authors.