Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Less is More: Contextual Sampling for Nonlinear Data-Driven Predictive Control

Julius Beerwerth, Bassam Alrifaee

TL;DR

This work tackles the real-time feasibility challenge of nonlinear Data-Driven Predictive Control (DeePC) by introducing Contextual Sampling, a dynamic data-selection strategy that chooses the most relevant trajectories based on the current state and upcoming reference. By forming a reduced mosaic-Hankel data matrix from a carefully selected subset, the approach preserves predictive accuracy while significantly lowering computational load. The method is validated on two robotics platforms—a scaled vehicle and a quadrotor—showing that Contextual Sampling matches or exceeds Random Sampling performance and approaches full DeePC accuracy with much less computation, and offering a favorable trade-off against more expensive Select-DPC. The results support the viability of data-efficient DeePC for real-time nonlinear robotic control, with ongoing work to establish theoretical guarantees and extend to higher-dimensional systems.

Abstract

Data-Driven Predictive Control (DPC) optimizes system behavior directly from measured trajectories without requiring an explicit model. However, its computational cost scales with dataset size, limiting real-time applicability to nonlinear robotic systems. For robotic tasks such as trajectory tracking and motion planning, real-time feasibility and numerical robustness are essential. Nonlinear DPC often relies on large datasets or learned nonlinear representations to ensure accuracy, both of which increase computational demand. We propose Contextual Sampling, a dynamic data selection strategy that adaptively selects the most relevant trajectories based on the current state and reference. By reducing dataset size while preserving representativeness, it improves computational efficiency. Experiments on a scaled autonomous vehicle and a quadrotor show that Contextual Sampling achieves comparable or better tracking than Random Sampling with fewer trajectories, enabling real-time feasibility. Compared with Select-DPC, it achieves similar tracking accuracy at lower computational cost. In comparison with the full DPC formulation without sampling, Contextual Sampling attains comparable tracking performance while requiring less computation, highlighting the benefit of efficient data selection in data-driven predictive control.

Less is More: Contextual Sampling for Nonlinear Data-Driven Predictive Control

TL;DR

This work tackles the real-time feasibility challenge of nonlinear Data-Driven Predictive Control (DeePC) by introducing Contextual Sampling, a dynamic data-selection strategy that chooses the most relevant trajectories based on the current state and upcoming reference. By forming a reduced mosaic-Hankel data matrix from a carefully selected subset, the approach preserves predictive accuracy while significantly lowering computational load. The method is validated on two robotics platforms—a scaled vehicle and a quadrotor—showing that Contextual Sampling matches or exceeds Random Sampling performance and approaches full DeePC accuracy with much less computation, and offering a favorable trade-off against more expensive Select-DPC. The results support the viability of data-efficient DeePC for real-time nonlinear robotic control, with ongoing work to establish theoretical guarantees and extend to higher-dimensional systems.

Abstract

Data-Driven Predictive Control (DPC) optimizes system behavior directly from measured trajectories without requiring an explicit model. However, its computational cost scales with dataset size, limiting real-time applicability to nonlinear robotic systems. For robotic tasks such as trajectory tracking and motion planning, real-time feasibility and numerical robustness are essential. Nonlinear DPC often relies on large datasets or learned nonlinear representations to ensure accuracy, both of which increase computational demand. We propose Contextual Sampling, a dynamic data selection strategy that adaptively selects the most relevant trajectories based on the current state and reference. By reducing dataset size while preserving representativeness, it improves computational efficiency. Experiments on a scaled autonomous vehicle and a quadrotor show that Contextual Sampling achieves comparable or better tracking than Random Sampling with fewer trajectories, enabling real-time feasibility. Compared with Select-DPC, it achieves similar tracking accuracy at lower computational cost. In comparison with the full DPC formulation without sampling, Contextual Sampling attains comparable tracking performance while requiring less computation, highlighting the benefit of efficient data selection in data-driven predictive control.

Paper Structure

This paper contains 15 sections, 1 theorem, 11 equations, 2 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contribution
  5. Structure
  6. Methodology
  7. Preliminaries
  8. Regularized deepc
  9. Contextual Sampling
  10. Implementation and Preprocessing
  11. Case Study: Trajectory Tracking for Vehicles and Quadrotors
  12. Experimental Setup
  13. Results
  14. Discussion
  15. Conclusion

Key Result

Lemma 1

(Fundamental Lemma, willems_note_2005coulson_data-enabled_2019) Consider a controllable system $\mathscr{B}$. Let $T, t \in \mathbb{Z}_{>0}$, and $w = \operatorname{col}(u,y) \in \mathscr{B}_T$. Assume $u$ to be persistently exciting of order $t+\bm{n}(\mathscr{B})$. Then

Figures (2)

  • Figure 1: Reference trajectories used in the case studies for the vehicle and quadrotor experiments.
  • Figure 2: Closed-loop tracking error distributions across different numbers of trajectories and sampling methods for (a) the vehicle and (b) the quadrotor.

Theorems & Definitions (2)

  • Definition 1: Persistency of Excitation, coulson_data-enabled_2019willems_note_2005
  • Lemma 1