This thesis considers the question of how to most effectively conduct experiments in Partially Observed Markov Decision Processes so as to provide data that is most informative about a parameter of interest. Methods from Markov decision processes, especially dynamic programming, are introduced and then used in algorithms to maximize a relevant Fisher Information. These algorithms are then applied to two POMDP examples. The methods developed can also be applied to stochastic dynamical systems, by suitable discretization, and we consequently show what control policies look like in the Morris-Lecar Neuron model and the Rosenzweig MacArthur Model, and simulation results are presented. We discuss how parameter dependence within these methods can be dealt with by the use of priors, and develop tools to update control policies online. This is demonstrated in another stochastic dynamical system describing growth dynamics of DNA template in a PCR model.