On the role of the signature transform in nonlinear systems and data-driven control

TL;DR

This paper explores the use of the signature transform as a novel feature extraction tool for representing and predicting nonlinear system trajectories, enabling a new data-driven predictive control approach.

Contribution

It introduces the signature transform into data-driven control, demonstrating its effectiveness for system representation and proposing a signature-based predictive control method.

Findings

Signature transform provides effective features for nonlinear systems.

The approach enables trajectory prediction without explicit system models.

A new data-driven control method based on signatures is proposed.

Abstract

Classic control techniques typically rely on a model of the system's response to external inputs, which is difficult to obtain from first principles especially if the unknown dynamics are nonlinear. In this paper, we address this issue by presenting an approach based on the so-called signature transform, a tool that is still largely unexplored in data-driven control. We first show that the signature provides rigorous and practically effective features to represent and predict system trajectories. Furthermore, we propose a novel use of this tool on an output-matching problem, paving the way for signature-based, data-driven predictive control.