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Data-Enabled Predictive Control for Flexible Spacecraft

Huanqing Wang, Kaixiang Zhang, Amin Vahidi-Moghaddam, Haowei An, Nan Li, Daning Huang, Zhaojian Li

TL;DR

This work introduces a data-driven DeePC framework for boundary control of a flexible spacecraft, leveraging Willems' fundamental lemma to build a non-parametric input-output model from past trajectories and addressing nonlinear, coupled PDE-ODE dynamics without explicit physics-based modeling. A dimension-reduction step using SVD is employed to keep the optimization tractable for real-time control, while regularization and slack handling improve robustness to noise and disturbances. Through FE-based simulations, DeePC is compared with a Lyapunov-based controller, showing comparable or superior angle-tracking performance and effective vibration suppression under nominal, uncertain, and noisy conditions, with DeePC displaying greater robustness to model mismatch. The results suggest a practical, model-free alternative for complex aerospace systems, reducing design time and enabling adaptive, data-driven control of flexible space structures.

Abstract

Spacecraft are vital to space exploration and are often equipped with lightweight, flexible appendages to meet strict weight constraints. These appendages pose significant challenges for modeling and control due to their inherent nonlinearity. Data-driven control methods have gained traction to address such challenges. This paper introduces, to the best of the authors' knowledge, the first application of the data-enabled predictive control (DeePC) framework to boundary control for flexible spacecraft. Leveraging the fundamental lemma, DeePC constructs a non-parametric model by utilizing recorded past trajectories, eliminating the need for explicit model development. The developed method also incorporates dimension reduction techniques to enhance computational efficiency. Through comprehensive numerical simulations, this study compares the proposed method with Lyapunov-based control, demonstrating superior performance and offering a thorough evaluation of data-driven control for flexible spacecraft.

Data-Enabled Predictive Control for Flexible Spacecraft

TL;DR

This work introduces a data-driven DeePC framework for boundary control of a flexible spacecraft, leveraging Willems' fundamental lemma to build a non-parametric input-output model from past trajectories and addressing nonlinear, coupled PDE-ODE dynamics without explicit physics-based modeling. A dimension-reduction step using SVD is employed to keep the optimization tractable for real-time control, while regularization and slack handling improve robustness to noise and disturbances. Through FE-based simulations, DeePC is compared with a Lyapunov-based controller, showing comparable or superior angle-tracking performance and effective vibration suppression under nominal, uncertain, and noisy conditions, with DeePC displaying greater robustness to model mismatch. The results suggest a practical, model-free alternative for complex aerospace systems, reducing design time and enabling adaptive, data-driven control of flexible space structures.

Abstract

Spacecraft are vital to space exploration and are often equipped with lightweight, flexible appendages to meet strict weight constraints. These appendages pose significant challenges for modeling and control due to their inherent nonlinearity. Data-driven control methods have gained traction to address such challenges. This paper introduces, to the best of the authors' knowledge, the first application of the data-enabled predictive control (DeePC) framework to boundary control for flexible spacecraft. Leveraging the fundamental lemma, DeePC constructs a non-parametric model by utilizing recorded past trajectories, eliminating the need for explicit model development. The developed method also incorporates dimension reduction techniques to enhance computational efficiency. Through comprehensive numerical simulations, this study compares the proposed method with Lyapunov-based control, demonstrating superior performance and offering a thorough evaluation of data-driven control for flexible spacecraft.

Paper Structure

This paper contains 14 sections, 1 theorem, 70 equations, 9 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Description
  3. DeePC Formulation and Control design
  4. Data-Enabled Predictive Control
  5. Dimension Reduction for DeePC
  6. Simulations
  7. Setup and Data Collection
  8. Benchmark Approach: Lyapunov-based Control Tracking Results
  9. Proposed Approach: DeePC Tracking Results
  10. Nominal Case
  11. Model Uncertainty and Process Noise
  12. Conclusion
  13. Finite Element Model for the Flexible Spacecraft
  14. Proof of Lyapunov Function

Key Result

Lemma 1

Let a sequence $(u_{[0,T-1]}^{\mathrm{d}}$$y_{[0,T-1]}^{\mathrm{d}})$ be an input/output trajectory of controllable LTI system eq:parametric_description, where $u_{[0,T-1]}^{\mathrm{d}}$ is persistently exciting of order $n + L$. Then, any length-$L$ sequence $(u_{[0,L-1]}, y_{[0,L-1]})$ is an input

Figures (9)

  • Figure 1: Schematic of the top view of the flexible spacecraft.
  • Figure 2: The angle and end-point deflection of the flexible appendage under no control.
  • Figure 3: The deformation of the flexible appendage under no control.
  • Figure 4: The performance comparison between DeePC and Lyapunov-based control under nominal case.
  • Figure 5: The deformation of the flexible spacecraft with Lyapunov-based control vs DeePC control under nominal conditions.
  • ...and 4 more figures

Theorems & Definitions (2)

  • Definition 1
  • Lemma 1: Fundamental Lemma WILLEMS2005325