On a probabilistic approach to synthesize control policies from example datasets

TL;DR

This paper presents a probabilistic method to synthesize control policies from example datasets, ensuring system behavior similarity and constraint compliance, even with noisy data and system differences.

Contribution

It introduces a theoretical framework and an explicit algorithm to derive control policies from example data, addressing actuation constraints and system discrepancies.

Findings

Effective control policy synthesis from real-world data

Guarantees system behavior similarity and constraint adherence

Validated with a highway merging case study

Abstract

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 theoretical 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.