# Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Control

arXiv: https://arxiv.org/abs/2112.12999 · HTML: https://mlsanity.com/paper/2112.12999/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 20 references that are in the map.
- First posted on arXiv 24 Dec 2021.

## Builds on (most cited first, 8 of 8)

- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Universal Approximation Theorems for Differentiable Geometric Deep Learning](https://mlsanity.com/paper/2101.05390/) (2021)
- [Stabilizing Neural Control Using Self-Learned Almost Lyapunov Critics](https://mlsanity.com/paper/2107.04989/) (2021)
- [Computing Lyapunov functions using deep neural networks](https://mlsanity.com/paper/2005.08965/) (2020)
- [Optimal Energy Shaping via Neural Approximators](https://mlsanity.com/paper/2101.05537/) (2021)

## Built on by (most cited first, 5 of 5)

- [Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2212.00893/) (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)
- [Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networks](https://mlsanity.com/paper/2412.11215/) (2024)
- [Robust Neural IDA-PBC: passivity-based stabilization under approximations](https://mlsanity.com/paper/2409.16008/) (2024)
- [Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control](https://mlsanity.com/paper/2604.26172/) (2026)

## Abstract (arXiv)

In this work we exploit the universal approximation property of Neural Networks (NNs) to design interconnection and damping assignment (IDA) passivity-based control (PBC) schemes for fully-actuated mechanical systems in the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC method into a supervised learning problem that solves the partial differential matching equations, and fulfills equilibrium assignment and Lyapunov stability conditions. A main consequence of this, is that the output of the learning algorithm has a clear control-theoretic interpretation in terms of passivity and Lyapunov stability. The proposed control design methodology is validated for mechanical systems of one and two degrees-of-freedom via numerical simulations.