A continuous-time fundamental lemma and its application in data-driven optimal control

TL;DR

This paper develops a new theoretical framework for data-driven optimal control of continuous-time linear systems, providing error bounds for polynomial approximations and demonstrating their impact on control performance.

Contribution

It introduces a continuous-time fundamental lemma and derives error bounds for polynomial approximations in data-driven control, linking latent variables and flat outputs.

Findings

Derived error bounds for polynomial approximations.

Characterized suboptimality in data-driven LQ control.

Numerical example illustrating theoretical results.

Abstract

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result, we rigorously derive error bounds for finite-order polynomial approximations of elements of the system behavior. To this end, we leverage a link between latent variables and flat outputs of controllable systems. Combined with a continuous-time counterpart of the fundamental lemma by Willems et al., we characterize the suboptimality resulting from polynomial approximations in data-driven linear-quadratic optimal control problems. Finally, we draw upon a numerical example to illustrate our results.