Optimal experiment design for identification of grey-box models

Optimal experiment design is investigated for stochastic dynamic systems where the prior partial information about the system is given as a probability distribution function in the system parameters. The concept of information is related to entropy reduction in the system through Lindley´s measure of average information, and the relationship between the choice of information related criteria and some estimators (MAP and MLE) is established. A continuous time physical model of the heat dynamics of a building is considered and the results show that performing an optimal experiment corresponding to a MAP estimation results in a considerable reduction of the experimental length. Besides, it is established that the physical knowledge of the system enables us to design experiments, with the goal of maximizing information about the physical parameters of interest.