From a Frequency-Domain Willems' Lemma to Data-Driven Predictive Control

TL;DR

This paper introduces a frequency-domain version of Willems' lemma, enabling data-driven predictive control using frequency data, which bridges existing methods and offers benefits like closed-loop data collection and visualization.

Contribution

It formulates a frequency-domain Willems' lemma, extends it to multiple data sets, and develops a novel frequency-domain data-driven predictive control scheme called FreePC.

Findings

FreePC is equivalent to DeePC under certain conditions.

Frequency-domain data enables closed-loop data collection.

The method offers computational and visualization advantages.

Abstract

Willems' fundamental lemma has recently received an impressive amount of attention from the data-driven control community. In this paper, we formulate a version of this celebrated result based on frequency-domain data. In doing so, we bridge the gap between recent developments in data-driven control, and the readily-available techniques and expertise for non-parametric frequency-domain identification. We also generalize our results to combine multiple frequency-domain data sets to form a sufficiently rich data set. Building on these results, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme provides a frequency-domain counterpart of the well-known data-enabled predictive control scheme DeePC based on time-domain data. Under appropriate conditions, the new frequency-domain data-driven predictive control (FreePC) scheme is equivalent to the corresponding DeePC scheme. We demonstrate the benefits of FreePC and the use of frequency-domain data in several examples and a numerical case study, including the ability to collect data in closed loop, computational benefits, and intuitive visualization of the data.