# Learning Reduced Nonlinear State-Space Models: an Output-Error Based Canonical Approach

arXiv: https://arxiv.org/abs/2206.04791 · HTML: https://mlsanity.com/paper/2206.04791/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 19 Apr 2022.

## Builds on (most cited first, 14 of 14)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting](https://mlsanity.com/paper/2010.04456/) (2020)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [NeuroBEM: Hybrid Aerodynamic Quadrotor Model](https://mlsanity.com/paper/2106.08015/) (2021)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [HybridNet: Integrating Model-based and Data-driven Learning to Predict Evolution of Dynamical Systems](https://mlsanity.com/paper/1806.07439/) (2018)
- [Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction](https://mlsanity.com/paper/2006.12682/) (2020)
- [Towards gain tuning for numerical KKL observers](https://mlsanity.com/paper/2204.00318/) (2022)
- [Deep KKL: Data-driven Output Prediction for Non-Linear Systems](https://mlsanity.com/paper/2103.12443/) (2021)
- [The Blackbird Dataset: A large-scale dataset for UAV perception in aggressive flight](https://mlsanity.com/paper/1810.01987/) (2018)
- [Learning to estimate UAV created turbulence from scene structure observed by onboard cameras](https://mlsanity.com/paper/2203.14726/) (2022)

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

- [Space and Time Continuous Physics Simulation From Partial Observations](https://mlsanity.com/paper/2401.09198/) (2024)

## Abstract (arXiv)

The identification of a nonlinear dynamic model is an open topic in control theory, especially from sparse input-output measurements. A fundamental challenge of this problem is that very few to zero prior knowledge is available on both the state and the nonlinear system model. To cope with this challenge, we investigate the effectiveness of deep learning in the modeling of dynamic systems with nonlinear behavior by advocating an approach which relies on three main ingredients: (i) we show that under some structural conditions on the to-be-identified model, the state can be expressed in function of a sequence of the past inputs and outputs; (ii) this relation which we call the state map can be modelled by resorting to the well-documented approximation power of deep neural networks; (iii) taking then advantage of existing learning schemes, a state-space model can be finally identified. After the formulation and analysis of the approach, we show its ability to identify three different nonlinear systems. The performances are evaluated in terms of open-loop prediction on test data generated in simulation as well as a real world data-set of unmanned aerial vehicle flight measurements.