# Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control

arXiv: https://arxiv.org/abs/2604.26172 · HTML: https://mlsanity.com/paper/2604.26172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [Unsupervised Learning of Lagrangian Dynamics from Images for Prediction and Control](https://mlsanity.com/paper/2007.01926/) (2020)
- [A Survey on Physics Informed Reinforcement Learning: Review and Open Problems](https://mlsanity.com/paper/2309.01909/) (2023)
- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [Stable Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2502.02480/) (2025)
- [Port-Hamiltonian Neural ODE Networks on Lie Groups For Robot Dynamics Learning and Control](https://mlsanity.com/paper/2401.09520/) (2024)
- [Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distribution](https://mlsanity.com/paper/2308.14666/) (2023)
- [Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Control](https://mlsanity.com/paper/2112.12999/) (2021)
- [Optimal Energy Shaping via Neural Approximators](https://mlsanity.com/paper/2101.05537/) (2021)
- [Learning Switching Port-Hamiltonian Systems with Uncertainty Quantification](https://mlsanity.com/paper/2305.09689/) (2023)
- [Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches](https://mlsanity.com/paper/2512.06315/) (2025)
- [Physics-Informed Multi-Agent Reinforcement Learning for Distributed Multi-Robot Problems](https://mlsanity.com/paper/2401.00212/) (2023)
- [Learning Neural Koopman Operators with Dissipativity Guarantees](https://mlsanity.com/paper/2509.07294/) (2025)
- [Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees](https://mlsanity.com/paper/2603.10078/) (2026)

## Abstract (arXiv)

We develop a physics-informed learning framework for energy-shaping control of port-Hamiltonian (pH) systems from trajectory data. The proposed approach co-learns a pH system model and an optimal energy-balancing passivity-based controller (EB-PBC) through alternating optimization with policy-aware data collection. At each iteration, the system model is refined using trajectory data collected under the current control policy, and the controller is re-optimized on the updated model. Both components are parameterized by neural networks that embed the pH dynamics and EB-PBC structure, ensuring interpretability in terms of energy interactions. The learned controller renders the closed-loop system inherently passive and provably stable, and exploits passive plant dynamics without canceling the natural potential. A dissipation regularization enforces strict energy decay during training, thereby enhancing robustness to sim-to-real gaps. The proposed framework is validated on state-regulation and swing-up tasks for planar and torsional pendulum systems.