Sensitivity and safety of fully probabilistic control

TL;DR

This paper conducts a sensitivity and safety analysis of the fully probabilistic control scheme, which optimizes control policies based on probability density functions, with implications for neural networks and reinforcement learning.

Contribution

It introduces a sensitivity analysis, characterizes the convergence region, and provides safety insights for the probabilistic control scheme, enhancing understanding of its robustness.

Findings

Characterizes the convergence region of the closed-loop system.

Provides a safety analysis for the probabilistic control scheme.

Illustrates results through simulations.

Abstract

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.