PREPRINT

Dimension Reduction for Efficient Data-Enabled Predictive Control

Kaixiang Zhang, Yang Zheng, Zhaojian Li

Submitted on 7 November 2022

Abstract

The recent data-enabled predictive control (DeePC) paradigm directly utilizes offline input/output data from an unknown system to predict its future trajectory and compute optimal control inputs online. In this scheme, the pre-collected input/output data needs to be sufficiently rich to represent the system behavior. This generally leads to an excessive amount of offline data, which consequently results in a high-dimension optimization problem in online predictive control. In this paper, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in DeePC. Specifically, in the case of linear time-invariant systems, the excessive input/output measurements can be rearranged into a smaller data library for the non-parametric representation of system behavior. Based on this observation, we use an SVD-based strategy to pre-process the offline data that achieves dimension reduction in DeePC. Numerical experiments confirm that the proposed method significantly enhances the computation efficiency without compromising the control performance.

Preprint

Comment: 9 pages, 4 figures

Subject: Electrical Engineering and Systems Science - Systems and Control

URL: http://arxiv.org/abs/2211.03697