# Robust Neural IDA-PBC: passivity-based stabilization under approximations

arXiv: https://arxiv.org/abs/2409.16008 · HTML: https://mlsanity.com/paper/2409.16008/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 24 Sep 2024.

## Builds on (most cited first, 12 of 12)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Physics-Informed Neural Nets for Control of Dynamical Systems](https://mlsanity.com/paper/2104.02556/) (2021)
- [Physics Informed Neural Networks for Control Oriented Thermal Modeling of Buildings](https://mlsanity.com/paper/2111.12066/) (2021)
- [Physics-informed Neural Networks-based Model Predictive Control for Multi-link Manipulators](https://mlsanity.com/paper/2109.10793/) (2021)
- [Critical Investigation of Failure Modes in Physics-informed Neural Networks](https://mlsanity.com/paper/2206.09961/) (2022)
- [Machine Learning Accelerated PDE Backstepping Observers](https://mlsanity.com/paper/2211.15044/) (2022)
- [Total Energy Shaping with Neural Interconnection and Damping Assignment -- Passivity Based Control](https://mlsanity.com/paper/2112.12999/) (2021)
- [Integral Action in Output Feedback for multi-input multi-output nonlinear systems](https://mlsanity.com/paper/1508.00476/) (2015)

## Built on by (most cited first, 1 of 1)

- [Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems](https://mlsanity.com/paper/2604.13297/) (2026)

## Abstract (arXiv)

In this paper, we restructure the Neural Interconnection and Damping Assignment - Passivity Based Control (Neural IDA-PBC) design methodology, and we formally analyze its closed-loop properties. Neural IDA-PBC redefines the IDA-PBC design approach as an optimization problem by building on the framework of Physics Informed Neural Networks (PINNs). However, the closed-loop stability and robustness properties under Neural IDA-PBC remain unexplored. To address the issue, we study the behavior of classical IDA-PBC under approximations. Our theoretical analysis allows deriving conditions for practical and asymptotic stability of the desired equilibrium point. Moreover, it extends the Neural IDA-PBC applicability to port-Hamiltonian systems where the matching conditions cannot be solved exactly. Our renewed optimization-based design introduces three significant aspects: i) it involves a novel optimization objective including stability and robustness constraints issued from our theoretical analysis; ii) it employs separate Neural Networks (NNs), which can be structured to reduce the search space to relevant functions; iii) it does not require knowledge about the port-Hamiltonian formulation of the system's model. Our methodology is validated with simulations on three standard benchmarks: a double pendulum, a nonlinear mass-spring-damper and a cartpole. Notably, classical IDA-PBC designs cannot be analytically derived for the latter.