On a probabilistic approach to synthesize control policies from example datasets

Davide Gagliardi, Giovanni Russo

Published 2020-05-22Version 1

This paper is concerned with the design of control policies from example data. The case considered is when only a probabilistic characterization of the system to be controlled is available and the system is affected by actuation constraints. These constraints are unknown to the demonstrators and hence might not be satisfied in the possibly noisy example data. In this context, we introduce a number of theoretical results to compute a control policy from the examples that: (i) makes the behavior of the closed-loop system similar to the one illustrated in the dataset; (ii) guarantees compliance with the constraints. The theoretical results give an explicit expression for the control policy and this allows to turn our findings into an algorithmic procedure. The procedure gives a systematic tool to compute the policy. The effectiveness of our approach is illustrated via a numerical example, where we use real data collected from test drives to synthesize a control policy for the merging of a car on a highway.