# Deep Lagrangian Networks for end-to-end learning of energy-based control for under-actuated systems

arXiv: https://arxiv.org/abs/1907.04489 · HTML: https://mlsanity.com/paper/1907.04489/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2019.

## Built on by (most cited first, 30 of 33)

- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
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- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Combining Physics and Deep Learning to learn Continuous-Time Dynamics Models](https://mlsanity.com/paper/2110.01894/) (2021)
- [Physics-Informed Model-Based Reinforcement Learning](https://mlsanity.com/paper/2212.02179/) (2022)
- [OSCAR: Data-Driven Operational Space Control for Adaptive and Robust Robot Manipulation](https://mlsanity.com/paper/2110.00704/) (2021)
- [Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems](https://mlsanity.com/paper/2211.16006/) (2022)
- [Continuous-Time Fitted Value Iteration for Robust Policies](https://mlsanity.com/paper/2110.01954/) (2021)
- [Diminishing Return of Value Expansion Methods in Model-Based Reinforcement Learning](https://mlsanity.com/paper/2303.03955/) (2023)
- [ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Bias](https://mlsanity.com/paper/2206.12325/) (2022)
- [A Black-Box Physics-Informed Estimator based on Gaussian Process Regression for Robot Inverse Dynamics Identification](https://mlsanity.com/paper/2310.06585/) (2023)
- [Symplectic Momentum Neural Networks -- Using Discrete Variational Mechanics as a prior in Deep Learning](https://mlsanity.com/paper/2201.08281/) (2022)
- [Discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2302.04400/) (2023)
- [MPC-Inspired Reinforcement Learning for Verifiable Model-Free Control](https://mlsanity.com/paper/2312.05332/) (2023)
- [Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.01916/) (2025)
- [End-to-End Learning of Hybrid Inverse Dynamics Models for Precise and Compliant Impedance Control](https://mlsanity.com/paper/2205.13804/) (2022)
- [A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from data](https://mlsanity.com/paper/2310.06241/) (2023)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Feasibility-aware Imitation Learning from Observations through a Hand-mounted Demonstration Interface](https://mlsanity.com/paper/2503.09018/) (2025)
- [Newtonian and Lagrangian Neural Networks: A Comparison Towards Efficient Inverse Dynamics Identification](https://mlsanity.com/paper/2506.17994/) (2025)
- [Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurements](https://mlsanity.com/paper/2512.03035/) (2025)
- [KeyCLD: Learning Constrained Lagrangian Dynamics in Keypoint Coordinates from Images](https://mlsanity.com/paper/2206.11030/) (2022)
- [Graph Neural Networks for Dynamic Modeling of Roller Bearing](https://mlsanity.com/paper/2309.10418/) (2023)
- [Joint torques prediction of a robotic arm using neural networks](https://mlsanity.com/paper/2405.00695/) (2024)
- [Diminishing Return of Value Expansion Methods](https://mlsanity.com/paper/2412.20537/) (2024)
- [ServoLNN: Lagrangian Neural Networks Driven by Servomechanisms](https://mlsanity.com/paper/2502.19802/) (2025)
- [Geometric Fault-Tolerant Neural Network Tracking Control of Unknown Systems on Matrix Lie Groups](https://mlsanity.com/paper/2505.04725/) (2025)
- [Feasibility-aware Imitation Learning from Observation with Multimodal Feedback](https://mlsanity.com/paper/2602.15351/) (2026)

## Abstract (arXiv)

Applying Deep Learning to control has a lot of potential for enabling the intelligent design of robot control laws. Unfortunately common deep learning approaches to control, such as deep reinforcement learning, require an unrealistic amount of interaction with the real system, do not yield any performance guarantees, and do not make good use of extensive insights from model-based control. In particular, common black-box approaches -- that abandon all insight from control -- are not suitable for complex robot systems. We propose a deep control approach as a bridge between the solid theoretical foundations of energy-based control and the flexibility of deep learning. To accomplish this goal, we extend Deep Lagrangian Networks (DeLaN) to not only adhere to Lagrangian Mechanics but also ensure conservation of energy and passivity of the learned representation. This novel extension is embedded within generic model-based control laws to enable energy control of under-actuated systems. The resulting DeLaN for energy control (DeLaN 4EC) is the first model learning approach using generic function approximation that is capable of learning energy control. DeLaN 4EC exhibits excellent real-time control on the physical Furuta Pendulum and learns to swing-up the pendulum while the control law using system identification does not.