# Robust Recurrent Neural Network to Identify Ship Motion in Open Water with Performance Guarantees -- Technical Report

arXiv: https://arxiv.org/abs/2212.05781 · HTML: https://mlsanity.com/paper/2212.05781/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Multi-Step Prediction of Dynamic Systems with Recurrent Neural Networks](https://mlsanity.com/paper/1806.00526/) (2018)
- [Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems](https://mlsanity.com/paper/2109.03861/) (2021)
- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Hybrid Physics and Deep Learning Model for Interpretable Vehicle State Prediction](https://mlsanity.com/paper/2103.06727/) (2021)

## Abstract (arXiv)

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this work, we represent a recurrent neural network as a linear time-invariant system with nonlinear disturbances. By introducing constraints on the parameters, we can guarantee finite gain stability and incremental finite gain stability. We apply this identification method to learn the motion of a four-degrees-of-freedom ship that is moving in open water and compare it against other purely learning-based approaches with unconstrained parameters. Our analysis shows that the constrained recurrent neural network has a lower prediction accuracy on the test set, but it achieves comparable results on an out-of-distribution set and respects stability conditions.