# Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator

arXiv: https://arxiv.org/abs/2410.01057 · HTML: https://mlsanity.com/paper/2410.01057/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 17 of 17)

- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-driven discovery of Koopman eigenfunctions for control](https://mlsanity.com/paper/1707.01146/) (2017)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Advantages of Bilinear Koopman Realizations for the Modeling and Control of Systems with Unknown Dynamics](https://mlsanity.com/paper/2010.09961/) (2020)
- [Model-Based Control Using Koopman Operators](https://mlsanity.com/paper/1709.01568/) (2017)
- [LMI Properties and Applications in Systems, Stability, and Control Theory](https://mlsanity.com/paper/1903.08599/) (2019)
- [Robust Tube-based Model Predictive Control with Koopman Operators--Extended Version](https://mlsanity.com/paper/2108.13011/) (2021)
- [Robust data-driven control for nonlinear systems using the Koopman operator](https://mlsanity.com/paper/2304.03519/) (2023)
- [Koopman-based feedback design with stability guarantees](https://mlsanity.com/paper/2312.01441/) (2023)
- [Koopman Linearization for Data-Driven Batch State Estimation of Control-Affine Systems](https://mlsanity.com/paper/2109.07000/) (2021)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Koopman Data-Driven Predictive Control with Robust Stability and Recursive Feasibility Guarantees](https://mlsanity.com/paper/2405.01292/) (2024)
- [Closed-Loop Koopman Operator Approximation](https://mlsanity.com/paper/2303.15318/) (2023)
- [Data-Driven Batch Localization and SLAM Using Koopman Linearization](https://mlsanity.com/paper/2309.04375/) (2023)
- [Dual-Loop Robust Control of Biased Koopman Operator Model by Noisy Data of Nonlinear Systems](https://mlsanity.com/paper/2401.08536/) (2024)

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

- [Koopman operator theory: fundamentals, control, and applications](https://mlsanity.com/paper/2607.01819/) (2026)

## Abstract (arXiv)

This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A finite-dimensional approximation of the Koopman operator can be identified directly from data, yielding an approximately linear model of a nonlinear system. The proposed observer synthesis method is made possible by this linearity that in turn allows uncertainty within a population of Koopman models to be quantified in the frequency domain. Using this uncertainty model, linear robust control techniques are used to synthesize robust nonlinear Koopman observers. A population of several dozen motor drives is used to experimentally demonstrate the proposed method. Manufacturing variation is characterized in the frequency domain, and a robust Koopman observer is synthesized using mixed H2-H_∞ optimal control.