# Linear Matrix Inequality Approaches to Koopman Operator Approximation

arXiv: https://arxiv.org/abs/2102.03613 · HTML: https://mlsanity.com/paper/2102.03613/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 6 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Modeling and Control of Soft Robots Using the Koopman Operator and Model Predictive Control](https://mlsanity.com/paper/1902.02827/) (2019)
- [LMI Properties and Applications in Systems, Stability, and Control Theory](https://mlsanity.com/paper/1903.08599/) (2019)
- [Learning Koopman Operator under Dissipativity Constraints](https://mlsanity.com/paper/1911.03884/) (2019)

## Built on by (most cited first, 2 of 2)

- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Closed-Loop Koopman Operator Approximation](https://mlsanity.com/paper/2303.15318/) (2023)

## Abstract (arXiv)

The regression problem associated with finding a matrix approximation of the Koopman operator from data is considered. The regression problem is formulated as a convex optimization problem subject to linear matrix inequality (LMI) constraints. Doing so allows for additional LMI constraints to be incorporated into the regression problem. In particular, asymptotic stability constraints, regularization using matrix norms, and even regularization using system norms can be easily incorporated into the regression problem.