Fast and memory-efficient optimization for large-scale data-driven predictive control

TL;DR

This paper introduces a fast, memory-efficient iterative solver for large-scale data-driven predictive control problems based on Willems' fundamental lemma, utilizing Fourier transform factorizations and an augmented Lagrangian method.

Contribution

It presents a novel solver that leverages Fourier-based factorizations and an augmented Lagrangian approach to improve efficiency and conditioning in data-driven predictive control.

Findings

The proposed method significantly reduces computation time.

It demonstrates improved memory efficiency over traditional approaches.

Numerical results validate the effectiveness of the solver.

Abstract

Recently, data-enabled predictive control (DeePC) schemes based on Willems' fundamental lemma have attracted considerable attention. At the core are computations using Hankel-like matrices and their connection to the concept of persistency of excitation. We propose an iterative solver for the underlying data-driven optimal control problems resulting from linear discrete-time systems. To this end, we apply factorizations based on the discrete Fourier transform of the Hankel-like matrices, which enable fast and memory-efficient computations. To take advantage of this factorization in an optimal control solver and to reduce the effect of inherent bad conditioning of the Hankel-like matrices, we propose an augmented Lagrangian lBFGS-method. We illustrate the performance of our method by means of a numerical study.