# Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach

arXiv: https://arxiv.org/abs/2112.09046 · HTML: https://mlsanity.com/paper/2112.09046/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 16 Dec 2021.

## Builds on (most cited first, 20 of 20)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [On orthogonality and learning recurrent networks with long term dependencies](https://mlsanity.com/paper/1702.00071/) (2017)
- [Orthogonal Recurrent Neural Networks with Scaled Cayley Transform](https://mlsanity.com/paper/1707.09520/) (2017)
- [Learning Decentralized Controllers for Robot Swarms with Graph Neural Networks](https://mlsanity.com/paper/1903.10527/) (2019)
- [Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Control](https://mlsanity.com/paper/2106.12782/) (2021)
- [Graph Policy Gradients for Large Scale Robot Control](https://mlsanity.com/paper/1907.03822/) (2019)
- [Hamiltonian Deep Neural Networks Guaranteeing Non-vanishing Gradients by Design](https://mlsanity.com/paper/2105.13205/) (2021)
- [An Ode to an ODE](https://mlsanity.com/paper/2006.11421/) (2020)
- [Offset-free setpoint tracking using neural network controllers](https://mlsanity.com/paper/2011.14006/) (2020)
- [Communication Topology Co-Design in Graph Recurrent Neural Network Based Distributed Control](https://mlsanity.com/paper/2104.13868/) (2021)
- [Graph Neural Networks for Distributed Linear-Quadratic Control](https://mlsanity.com/paper/2011.05360/) (2020)
- [Learning Deep Energy Shaping Policies for Stability-Guaranteed Manipulation](https://mlsanity.com/paper/2103.16432/) (2021)
- [A unified framework for Hamiltonian deep neural networks](https://mlsanity.com/paper/2104.13166/) (2021)
- [A Unified Passivity-Based Framework for Control of Modular Islanded AC Microgrids](https://mlsanity.com/paper/2104.02637/) (2021)

## Built on by (most cited first, 12 of 12)

- [Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applications](https://mlsanity.com/paper/2206.07922/) (2022)
- [Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2212.00893/) (2022)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.06335/) (2023)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks](https://mlsanity.com/paper/2412.11215/) (2024)
- [L2RU: a Structured State Space Model with prescribed L2-bound](https://mlsanity.com/paper/2503.23818/) (2025)
- [Controller Design for Structured State-space Models via Contraction Theory](https://mlsanity.com/paper/2604.07069/) (2026)
- [Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systems](https://mlsanity.com/paper/2403.00381/) (2024)
- [Distributed Control of Network Systems in the Space of Stabilizing Graph Neural Network Policies](https://mlsanity.com/paper/2512.18540/) (2025)

## Abstract (arXiv)

Large-scale cyber-physical systems require that control policies are distributed, that is, that they only rely on local real-time measurements and communication with neighboring agents. Optimal Distributed Control (ODC) problems are, however, highly intractable even in seemingly simple cases. Recent work has thus proposed training Neural Network (NN) distributed controllers. A main challenge of NN controllers is that they are not dependable during and after training, that is, the closed-loop system may be unstable, and the training may fail due to vanishing and exploding gradients. In this paper, we address these issues for networks of nonlinear port-Hamiltonian (pH) systems, whose modeling power ranges from energy systems to non-holonomic vehicles and chemical reactions. Specifically, we embrace the compositional properties of pH systems to characterize deep Hamiltonian control policies with built-in closed-loop stability guarantees, irrespective of the interconnection topology and the chosen NN parameters. Furthermore, our setup enables leveraging recent results on well-behaved neural ODEs to prevent the phenomenon of vanishing gradients by design. Numerical experiments corroborate the dependability of the proposed architecture, while matching the performance of general neural network policies.