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Datamodel-Based Data Selection for Nonlinear Data-Enabled Predictive Control

Jiachen Li, Shihao Li, Dongmei Chen

TL;DR

This work tackles data selection for nonlinear DeePC by introducing a context-dependent linear datamodel that maps initial trajectory and reference trajectory to column-inclusion scores. A neural network amortizes the context-to-influence mapping, enabling online Top-K selection that reduces the DeePC problem from using all Hankel columns to a small, task-relevant subset. Offline training uses closed-loop simulations to learn how column inclusion impacts cost across tasks, demonstrating substantial performance gains over geometry-based selection, especially at small subset sizes, while maintaining convergence toward full-data performance as data grows. The approach provides a scalable, task-aware framework for data-driven control in nonlinear systems with explicit online integration into DeePC.

Abstract

Data-Enabled Predictive Control (DeePC) has emerged as a powerful framework for controlling unknown systems directly from input-output data. For nonlinear systems, recent work has proposed selecting relevant subsets of data columns based on geometric proximity to the current operating point. However, such proximity-based selection ignores the control objective: different reference trajectories may benefit from different data even at the same operating point. In this paper, we propose a datamodel-based approach that learns a context-dependent influence function mapping the current initial trajectory and reference trajectory to column importance scores. Adapting the linear datamodel framework from machine learning, we model closed-loop cost as a linear function of column inclusion indicators, with coefficients that depend on the control context. Training on closed-loop simulations, our method captures which data columns actually improve tracking performance for specific control tasks. Experimental results demonstrate that task-aware selection substantially outperforms geometry-based heuristics, particularly when using small data subsets.

Datamodel-Based Data Selection for Nonlinear Data-Enabled Predictive Control

TL;DR

This work tackles data selection for nonlinear DeePC by introducing a context-dependent linear datamodel that maps initial trajectory and reference trajectory to column-inclusion scores. A neural network amortizes the context-to-influence mapping, enabling online Top-K selection that reduces the DeePC problem from using all Hankel columns to a small, task-relevant subset. Offline training uses closed-loop simulations to learn how column inclusion impacts cost across tasks, demonstrating substantial performance gains over geometry-based selection, especially at small subset sizes, while maintaining convergence toward full-data performance as data grows. The approach provides a scalable, task-aware framework for data-driven control in nonlinear systems with explicit online integration into DeePC.

Abstract

Data-Enabled Predictive Control (DeePC) has emerged as a powerful framework for controlling unknown systems directly from input-output data. For nonlinear systems, recent work has proposed selecting relevant subsets of data columns based on geometric proximity to the current operating point. However, such proximity-based selection ignores the control objective: different reference trajectories may benefit from different data even at the same operating point. In this paper, we propose a datamodel-based approach that learns a context-dependent influence function mapping the current initial trajectory and reference trajectory to column importance scores. Adapting the linear datamodel framework from machine learning, we model closed-loop cost as a linear function of column inclusion indicators, with coefficients that depend on the control context. Training on closed-loop simulations, our method captures which data columns actually improve tracking performance for specific control tasks. Experimental results demonstrate that task-aware selection substantially outperforms geometry-based heuristics, particularly when using small data subsets.

Paper Structure

This paper contains 30 sections, 20 equations, 1 figure, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Setting
  4. Hankel Matrices
  5. Standard DeePC Formulation
  6. Linear Datamodel Framework
  7. The Datamodeling Paradigm
  8. Linear Datamodel Formulation
  9. Adaptation to DeePC Column Selection
  10. Optimal Column Selection
  11. Estimation via Regression
  12. Context-Dependent Datamodels
  13. Motivation: Why Context Matters
  14. Context-Dependent Linear Datamodel
  15. Parameterization via Neural Networks
  16. ...and 15 more sections

Figures (1)

  • Figure 1: Closed-loop cost versus number of selected columns on the Reacher environment ($M = 36{,}800$ total columns). Line styles indicate selection methods (solid: Datamodel, dash-dot: $L_1$, dotted: Isomap, dashed: Random). Colors indicate cost metrics (blue: Cost, orange: IAE, green: ISE). Lower is better. Our datamodel-based approach achieves approximately $2\times$ lower cost than geometric baselines at small subset sizes.