Optimal experiment design with applications to Pharmacokinetic modeling

We study the problem of designing an input to a dynamical system that is optimal at estimating unknown parameters in the system's model. We take the A and D optimality criteria on the Fisher Information Matrix associated with the estimation problem as our optimization objective. Our main motivation is the estimation of the physiological parameters that appear in pharmacokinetic dynamics using a relatively short set of measurements. In this context, model inputs correspond to the intravenous injection of drugs and input selection needs to consider safety constraints that include max-min instantaneous injection rates and total dosage amount. We divide the time interval available for the experiment into learning and optimization stages. We use the initial learning stage to obtain a preliminary estimate for the system's model. Then we find an optimal input for the optimization stage so that we can improve upon this initial estimate.