Frequency-Domain Data-Driven Predictive Control

TL;DR

The paper addresses the gap between time-domain data-driven predictive control and the rich frequency-domain identification toolbox. It introduces FreePC, a spectral-data based predictive control framework built on a frequency-domain Willems' fundamental lemma, and proves its nominal equivalence to DeePC. The approach enables leveraging frequency-domain data such as FRFs and reduces optimization complexity by tying decision variables to the number of frequency samples rather than data length. Numerical results on an unstable SISO plant show FreePC can closely match model-based performance, with accuracy improving as more frequency samples are used, and illustrate practical benefits in data collection through frequency-domain methods.

Abstract

In this paper, we propose a data-driven predictive control scheme based on measured frequency-domain data of the plant. This novel scheme complements the well-known data-driven predictive control (DeePC) approach based on time series data. To develop this new frequency-domain data-driven predictive control (FreePC) scheme, we introduce a novel version of Willems' fundamental lemma based on frequency-domain data. By exploiting frequency-domain data, we allow recent direct data-driven (predictive) control methodologies to benefit from the available expertise and techniques for non-parametric frequency-domain identification in academia and industry. We prove that, under appropriate conditions, the new FreePC scheme is equivalent to the corresponding DeePC scheme. The strengths of FreePC are demonstrated in a numerical case study.

Figures (3)

• Figure 1: Closed-loop measurement setup.
• Figure 2: Estimated FRF of the true system () using $P=2$ periods ($\bm{\cdot}$) and $P=50$ periods ($\bm{\cdot}$) along with their respective $99\%$ confidence intervals (/).
• Figure 3: Comparison of FreePC using data containing $P=2$ periods () and $P=50$ periods () along with a model-based benchmark ().