Core Concepts
Efficient recursive updating algorithm for DeePC using SVD.
Abstract
The content introduces a novel recursive updating algorithm for Data-enabled Predictive Control (DeePC) utilizing Singular Value Decomposition (SVD) for efficient low-dimensional transformations. It addresses challenges in computational demand due to recursive data updates and demonstrates flexibility in encompassing various data-driven methods. The paper outlines the methodology, validation through simulation studies, and comparisons with Subspace Predictive Control.
I. Introduction
Model Predictive Control (MPC) and DeePC significance.
Challenges with increased computational demand in DeePC.
Introduction of a novel recursive updating algorithm using SVD.
II. Preliminaries
Linear Time-Invariant (LTI) system description.
Hankel matrix definition and Willems’ Fundamental Lemma.
III. Efficient Recursive Updates in the DeePC Framework
Equivalent low-dimensional transformation using SVD.
Fast SVD updating technique.
Algorithm 3 summary for efficient recursive DeePC.
IV. Extension to Data-driven Methods Based on Pseudoinverse
Versatility of the proposed algorithm for various data-driven methodologies.
Comparison to Subspace Predictive Control.
V. Simulation
Evaluation of the proposed algorithm's effectiveness through simulation studies on an LTI system.
Appendix A: Proof of Lemmas 7 and 8 for consistency analysis.
Appendix B: Data-driven prediction formulation in specific form (13).
Appendix C: Integration of forgetting factors for adaptive DeePC algorithms.
Appendix D: Equivalent formulations for Pseudoinverse-based output prediction.
Stats
Recent studies have aimed to mitigate computational overhead by reducing dimensions of decision variables using Singular Value Decomposition (SVD).