Robust Direct Data-Driven Control for Probabilistic Systems

TL;DR

This paper introduces a data-driven control approach for probabilistic systems with aleatoric uncertainty, emphasizing robustness and transferability without prior parameter estimation, validated through theoretical bounds and numerical examples.

Contribution

It presents a novel scenario optimization-based method that guarantees robustness and generalization for probabilistic systems using shared trajectory data.

Findings

Controllers generalize well to high variations with limited data

The method guarantees quadratic stability under data bounds

Robust controllers enable safe deployment without further learning

Abstract

We propose a data-driven control method for systems with aleatoric uncertainty, for example, robot fleets with variations between agents. Our method leverages shared trajectory data to increase the robustness of the designed controller and thus facilitate transfer to new variations without the need for prior parameter and uncertainty estimations. In contrast to existing work on experience transfer for performance, our approach focuses on robustness and uses data collected from multiple realizations to guarantee generalization to unseen ones. Our method is based on scenario optimization combined with recent formulations for direct data-driven control. We derive lower bounds on the amount of data required to achieve quadratic stability for probabilistic systems with aleatoric uncertainty and demonstrate the benefits of our data-driven method through a numerical example. We find that the learned controllers generalize well to high variations in the dynamics even when based on only a few short open-loop trajectories. Robust experience transfer enables the design of safe and robust controllers that work out of the box without any additional learning during deployment.