Sensitivity and safety of fully probabilistic control

In this paper we present a sensitivity analysis for the so-called fully probabilistic control scheme. This scheme attempts to control a system modeled via a probability density function (pdf) and does so by computing a probabilistic control policy that is optimal in the Kullback-Leibler sense. Situations where a system of interest is modeled via a pdf naturally arise in the context of neural networks, reinforcement learning and data-driven iterative control. After presenting the sensitivity analysis, we focus on characterizing the convergence region of the closed loop system and introduce a safety analysis for the scheme. The results are illustrated via simulations. This is the preliminary version of the paper entitled "On robust stability of fully probabilistic control with respect to data-driven model uncertainties" that will be presented at the 2019 European Control Conference.