Designing robust optimal dynamic experiments

The quality of experiments designed using standard optimisation-based techniques can be adversely affected by poor starting values of the parameters. Thus, there is a necessity for design methods that are insensitive (“robust”) to these starting values. Here, two novel, robust criteria are presented for computing optimal dynamic inputs for experiments aiming at improving parameter precision, based on previously proposed methods for providing design robustness — the expected value criterion and the max–min criterion. In this paper, both criteria are extended by use of the information matrix derived for dynamic systems. The experiment design problem is cast as an optimal control problem, with experiment decision variables such as sampling times of response variables, time-varying and time-invariant external controls, experiment duration, and initial conditions. Comparisons are made of experiment designs obtained using the conventional approach and the newly proposed criteria. A typical semi-continuous bioreactor application is presented.