A Review of Probabilistic Control and Majorization of Optimal Control

In probabilistic control a controller is designed by matching modelled with some arbitrary but desired closed-loop system trajectory distribution. In thisworkwe reviewseveral productive approaches to measure the proximity between probable and desired behaviour. We then illustrate how the associated optimization problems solve into uncertain policies. Our main result is to show that these probabilistic control objectives majorize conventional, stochastic and risk sensitive, optimal control objectives. This observation allows us to identify two probabilistic fixed point iterations that converge to the deterministic optimal control policies. Based on these insights we discuss directions for future algorithmic development and point out some remaining challenges.