Hybrid Model Predictive Control with Physics-Informed Neural Network for Satellite Attitude Control

Technical Deep Dive: Hybrid Model Predictive Control with Physics-Informed Neural Network for Satellite Attitude Control

Overview

This work explores the use of Physics-Informed Neural Networks (PINNs) to model spacecraft attitude dynamics and embed the learned models within a hybrid Model Predictive Control (MPC) framework for improved satellite attitude control. The key contributions are:

• Development of a PINN-based learning framework to model spacecraft attitude dynamics, with a physics-informed loss function that enhances robustness and generalization.
• Systematic comparison of purely data-driven and physics-constrained learning, demonstrating a 68.17% reduction in mean relative error over 10-step recursive prediction horizons.
• Validation of the control relevance of the learned models by embedding them into a hybrid PINN + linear MPC scheme, achieving improved closed-loop performance under realistic disturbances.

Problem & Context

• Reliable spacecraft attitude control depends on accurate prediction of attitude dynamics, particularly for model-based controllers like MPC.
• Obtaining accurate physics-based models for spacecraft with complex dynamics can be difficult, time-consuming, or computationally heavy.
• Learning-based system identification presents a compelling alternative, but models trained exclusively on data often exhibit fragile stability properties and limited extrapolation capability.
• This work proposes a hybrid modeling approach that combines physical knowledge with data-driven learning using PINNs.

Methodology

Satellite Attitude Dynamics

• The dynamics are governed by the spacecraft inertia, reaction wheel inertia, angular velocities, control torques, and external disturbance torques.
• The equations of motion describe the evolution of the spacecraft and reaction wheel angular velocities, as well as the quaternion representation of the attitude.

Neural Network Architecture

• A multilayer perceptron (MLP) neural network is used to learn the spacecraft attitude dynamics.
• The model input includes the spacecraft inertia matrix, current state (satellite and reaction wheel angular velocities), and angular acceleration.
• The network outputs the predicted trajectory of angular velocity changes over a 10-step horizon.

Physics-Informed Training

• The training objective combines a data-driven loss (normalized RMSE of angular velocity prediction) and a physics-informed loss.
• The physics-informed loss regularizes the model by enforcing consistency with the governing attitude dynamics equations, including angular acceleration and angular momentum conservation.
• A Lagrangian dual strategy is used to adaptively adjust the relative importance of the data-driven and physics-informed losses.

Hybrid MPC with Learned Dynamics

• The trained PINN model is integrated into a nonlinear MPC framework to enable attitude control.
• When the attitude error falls below 1 degree, the MPC switches from using the nonlinear PINN model to a linear state-space model for improved steady-state convergence.
• The MPC cost function penalizes attitude error, control effort, and control effort variation.

Data & Experimental Setup

• The dataset is generated using high-fidelity numerical simulations in the Basilisk framework, considering a cubesat in Low Earth Orbit actuated by reaction wheels and subjected to environmental disturbances.
• The dataset includes 300 nominal simulations and an additional 50 simulations with parameter variations (±10% in satellite mass and inertia).
• The neural network models are trained and evaluated on this dataset, with a 67-33% split for training and validation.
• Comparison is made against two traditional MPC baselines: a linear state-space MPC and a nonlinear MPC.
• Evaluation is performed through 300 Monte Carlo simulations, introducing state estimation noise, parameter uncertainty, and reaction wheel friction.

Results

Attitude Dynamics Regressor

• The physics-informed model (MLP-LD) achieves a 68.17% reduction in mean relative error compared to the purely data-driven model (MLP-DD) for 10-step recursive predictions.
• The improvements in both mean relative error and physics-informed loss are statistically significant.

MPC Controllers

• The hybrid MPC scheme (MLP-LD + Linear) outperforms the purely nonlinear MPC and linear MPC in terms of settling time, reducing it by 61.52%-76.42% under the tested noise and uncertainty conditions.
• The hybrid MPC achieves comparable steady-state error to the linear MPC, but requires significantly higher reaction wheel torques.

Interpretation

• Embedding physical constraints into the neural network training process through the physics-informed loss function substantially enhances the model's predictive accuracy and control-relevant properties.
• The hybrid MPC framework, which transitions from the nonlinear PINN model to a linear state-space model at low attitude errors, achieves the best overall performance, balancing fast convergence and low steady-state error.
• The higher reaction wheel torques required by the hybrid MPC suggest a trade-off between control effort and convergence speed that could be further explored.

Limitations & Uncertainties

• The dataset, while comprehensive, is still limited to a specific cubesat platform and set of disturbances. Extrapolation to more complex spacecraft or environments may require further validation.
• The study focuses on rest-to-rest maneuvers; the performance of the learned models and hybrid MPC may differ for more complex attitude trajectories.
• The experiments consider parameter uncertainties up to 20%, but real-world spacecraft may experience larger variations over their lifetime.

What Comes Next

• Extending the framework to handle more complex spacecraft dynamics, such as flexible appendages or non-rigid bodies.
• Exploring the use of PINNs for modeling discontinuous dynamics, partial observability, and restricted actuation, as encountered in satellite berthing or docking with non-cooperative targets.
• Investigating the trade-offs between control effort and convergence speed in the hybrid MPC formulation, potentially through multi-objective optimization.
• Validating the approach on real-world hardware-in-the-loop experiments or actual spacecraft missions.