# Learning Data-Driven Stable Koopman Operators

@article{Mamakoukas2020LearningDS, title={Learning Data-Driven Stable Koopman Operators}, author={Giorgos Mamakoukas and Ian Abraham and Todd D. Murphey}, journal={ArXiv}, year={2020}, volume={abs/2005.04291} }

In this paper, we consider the problem of improving the long-term accuracy of data-driven approximations of Koopman operators, which are infinite-dimensional linear representations of general nonlinear systems, by bounding the eigenvalues of the linear operator. We derive a formula for the global error of general Koopman representations and motivate imposing stability constraints on the data-driven model to improve the approximation of nonlinear systems over a longer horizon. In addition…

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## 9 Citations

System Norm Regularization Methods for Koopman Operator Approximation

- Computer ScienceArXiv
- 2021

DMD and DMD with control are reformulated as convex optimization problems with linear matrix inequality constraints and hard asymptotic stability constraints and system norm regularizers are considered as methods to improve the numerical conditioning of the approximate Koopman operator.

Efficient Learning of a Linear Dynamical System with Stability Guarantees

- Mathematics, Computer ScienceArXiv
- 2021

This work proposes a principled method for projecting an arbitrary square matrix to the nonconvex set of asymptotically stable matrices and shows that this projection is optimal in an information-theoretic sense and simply amounts to shifting the initial matrix by an optimal linear quadratic feedback gain.

Data-Driven Safety-Critical Control: Synthesizing Control Barrier Functions With Koopman Operators

- Computer Science, MathematicsIEEE Control Systems Letters
- 2021

This work proposes to learn discrete-time Koopman operators of the closed-loop dynamics under a backup strategy, and derives an error bound on the unmodeled dynamics in order to robustify the CBF controller.

Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

- EngineeringIEEE Robotics and Automation Letters
- 2022

A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator, where a cost functional is minimized as a convex optimization problem thanks to the linear dynamics in the lifted space.

Physics-informed machine learning: case studies for weather and climate modelling

- Environmental SciencePhilosophical Transactions of the Royal Society A
- 2021

This work surveys systematic approaches to incorporating physics and domain knowledge into ML models and distill these approaches into broad categories, and shows how these approaches have been used successfully for emulating, downscaling, and forecasting weather and climate processes.

Learning Data-Driven PCHD Models for Control Engineering Applications

- Computer Science, EngineeringArXiv
- 2022

This work exploits the advantages of both strategies and presents a new framework to obtain nonlinear high accurate system models in a data-driven way that are directly in PCHD form.

Data-Driven Models for Control Engineering Applications Using the Koopman Operator

- Engineering, Computer ScienceArXiv
- 2021

This work investigates how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications and shows how relevant system properties like stability, controllability, and observability are reflected by the EDMD model.

Derivative-Based Koopman Operators for Real-Time Control of Robotic Systems

- MathematicsIEEE Transactions on Robotics
- 2021

Experimental results show that the proposed data-driven control approach outperforms a tuned proportional–integral–derivative controller and that updating the data- driven model online significantly improves performance in the presence of unmodeled fluid disturbance.

On the Equivalence of Contraction and Koopman Approaches for Nonlinear Stability and Control

- Mathematics2021 60th IEEE Conference on Decision and Control (CDC)
- 2021

Equivalence between contraction and Koopman approaches for a wide class of stability analysis and control design problems is shown, in particular: stability or stablisability in the Koop man framework implies the existence of a contraction metric for the nonlinear system.

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