On a probabilistic approach to synthesize control policies from example datasets

This paper is concerned with the design of control policies from example datasets. The case considered is when just a black box description of the system to be controlled is available and the system is affected by actuation constraints. These constraints are not necessarily fulfilled by the (possibly, noisy) example data and the system under control is not necessarily the same as the one from which these data are collected. In this context, we introduce a number of methodological results to compute a control policy from example datasets that: (i) makes the behavior of the closed-loop system similar to the one illustrated in the data; (ii) guarantees compliance with the constraints. We recast the control problem as a finite-horizon optimal control problem and give an explicit expression for its optimal solution. Moreover, we 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.