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Extending direct data-driven predictive control towards systems with finite control sets

Manuel Klädtke, Moritz Schulze Darup, Daniel E. Quevedo

TL;DR

This paper addresses extending direct data-driven predictive control (DPC) to systems with finite control sets (FCS) by reformulating the FCS‑DPC problem to enable sphere decoding (SDA). It introduces implicit predictors to preserve predictive behavior under FCS constraints and derives an explicit SDA‑friendly OCP, showing affine, data-driven predictions that couple with a quadratic cost. A three‑level inverter drive example demonstrates that SDA provides faster computation times than enumeration or MIQP, albeit with variability, highlighting a path toward real-time FCS‑DPC in power electronics. The work suggests further extensions to nonlinear systems and deeper analysis of implicit predictors under various regularizers.

Abstract

Although classical model predictive control with finite control sets (FCS-MPC) is quite a popular control method, particularly in the realm of power electronics systems, its direct data-driven predictive control (FCS-DPC) counterpart has received relatively limited attention. In this paper, we introduce a novel reformulation of a commonly used DPC scheme that allows for the application of a modified sphere decoding algorithm, known for its efficiency and prominence in FCS-MPC applications. We test the reformulation on a popular electrical drive example and compare the computation times of sphere decoding FCS-DPC with an enumeration-based and a MIQP method.

Extending direct data-driven predictive control towards systems with finite control sets

TL;DR

This paper addresses extending direct data-driven predictive control (DPC) to systems with finite control sets (FCS) by reformulating the FCS‑DPC problem to enable sphere decoding (SDA). It introduces implicit predictors to preserve predictive behavior under FCS constraints and derives an explicit SDA‑friendly OCP, showing affine, data-driven predictions that couple with a quadratic cost. A three‑level inverter drive example demonstrates that SDA provides faster computation times than enumeration or MIQP, albeit with variability, highlighting a path toward real-time FCS‑DPC in power electronics. The work suggests further extensions to nonlinear systems and deeper analysis of implicit predictors under various regularizers.

Abstract

Although classical model predictive control with finite control sets (FCS-MPC) is quite a popular control method, particularly in the realm of power electronics systems, its direct data-driven predictive control (FCS-DPC) counterpart has received relatively limited attention. In this paper, we introduce a novel reformulation of a commonly used DPC scheme that allows for the application of a modified sphere decoding algorithm, known for its efficiency and prominence in FCS-MPC applications. We test the reformulation on a popular electrical drive example and compare the computation times of sphere decoding FCS-DPC with an enumeration-based and a MIQP method.
Paper Structure (10 sections, 2 theorems, 24 equations, 1 figure)

This paper contains 10 sections, 2 theorems, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Basics on FCS-MPC and DPC
  3. Basics on MPC
  4. Solving FCS-MPC via sphere decoding
  5. Basics on regularized DPC
  6. Applying sphere decoding to FCS-DPC
  7. An implicit predictor for FCS-DPC
  8. Reformulating FCS-DPC for sphere decoding
  9. Example
  10. Conclusion and Outlook

Key Result

Lemma 1

Under Assumption assum:fullRank, the regularized DPC problem eq:DPC is equivalent to with unique

Figures (1)

  • Figure 1: A boxplot showing computation times over 800 steps of closed-loop simulation. Crosses refer to outliers (all above the 75th percentile plus $1.5$ times the interquartile range).

Theorems & Definitions (7)

  • Remark 1
  • Definition 1: KLAEDTKE2023
  • Lemma 1: KLAEDTKE2023
  • Theorem 2
  • proof
  • Remark 2
  • Remark 3