Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements

TL;DR

The paper tackles physical inconsistency in learned Lagrangian models for non-conservative mechanical systems under limited/no acceleration data. It introduces an inverse-model–based loss L_prop that enforces torque consistency by integrating Euler–Lagrange relations along trajectories, avoiding direct acceleration measurements and remaining compatible with multiple hybrid models (DeLaN, APHYNITY, ADLN). Empirical results on a nonlinear mass–spring–damper and the Furuta pendulum show that L_prop improves energy fidelity, force decomposition, and control performance, enabling reliable swing-up and stabilization with energy-based and LQR controllers on both simulated and real FP data. The work provides a practical, physics-informed learning framework that enhances model quality for control in data-scarce, real-world settings.

Abstract

This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification of physically consistent models, which are essential for model-based control synthesis. Lagrangian or Hamiltonian neural networks provide useful structural guarantees but the learning of such models often leads to inconsistent models, especially on real physical systems where training data are limited, partial and noisy. Motivated by this observation and the objective to exploit these models for model-based nonlinear control, a learning algorithm relying on an original loss function is proposed to improve the physical consistency of Lagrangian systems. A comparative analysis of different learning-based modeling approaches with the proposed solution shows significant improvements in terms of physical consistency of the learned models, on both simulated and experimental systems. The model's consistency is then exploited to demonstrate, on an experimental benchmark, the practical relevance of the proposed methodology for feedback linearization and energy-based control techniques.

Figures (4)

• Figure 1: Trajectory prediction results for the different models on the first 10 seconds of each test set. For the experimental Furuta figure, only the proposed loss' results are shown for clarity.
• Figure 2: Energy function for all systems both across states and along a trajectory
• Figure 3: Force decomposition of the different models on an example of a forced trajectory. The generalized forces are represented on the $y$ axis and the time is on the $x$ axis.
• Figure 4: Swing up and stabilization of the real and simulated Furuta pendulum from the initial condition $x_0=(0, 0, 0, 0)^T$. SIMU represents the controller designed using the simulation model defined in section \ref{['sec:Benchmark systems and data generation']}.