Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements

2025-12-02

AI Summary

Existing neural network models for Lagrangian systems with non-conservative forces often violate physical consistency—particularly under conditions of no acceleration measurements, limited and noisy data—thereby hindering model-based control design. Method: We propose a hybrid learning framework that explicitly incorporates prior knowledge of system dynamics. Leveraging only position, velocity, and control input data, it introduces a novel physics-informed loss function that enforces Lagrangian structural constraints and energy evolution laws, thereby eliminating the need for acceleration estimation or numerical differentiation. Contribution/Results: The method significantly improves physical fidelity in both simulation and real-world experiments. It is the first to experimentally demonstrate support for high-precision feedback linearization and energy-shaping control, while maintaining robustness and practical deployability.

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• Machine Learning: Neuro-Symbolic Learning

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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.

Problem

• Learning physically consistent Lagrangian models without acceleration data
• Improving model consistency for model-based nonlinear control synthesis
• Enhancing physical consistency in learned models for control applications

Innovation

• Hybrid method eliminates acceleration measurements requirement
• Original loss function enhances Lagrangian model physical consistency
• Physically consistent models enable feedback linearization and energy-based control