# A Convex Optimization Approach to Learning Koopman Operators

@article{Sznaier2021ACO, title={A Convex Optimization Approach to Learning Koopman Operators}, author={Mario Sznaier}, journal={ArXiv}, year={2021}, volume={abs/2102.03934} }

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models. However, choosing appropriate models and bounding the approximation error is far from trivial. Motivated by these difficulties, in this paper we propose an optimization based approach to learning Koopman operators from data. Our results show that the Koopman…

## 3 Citations

Linear Matrix Inequality Approaches to Koopman Operator Approximation

- MathematicsArXiv
- 2021

Koopman operator theory [1–4] provides a means to globally represent a nonlinear system as a linear system by transforming its states into an infinite-dimensional space of lifted states. The Koopman…

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.

Control Oriented Learning in the Era of Big Data

- Computer ScienceIEEE Control Systems Letters
- 2021

The main message is twofold (i) computational complexity in control oriented learning is driven both by system order and the presence of uncertainty, rather than the dimension of the data, and (ii) exploiting the underlying sparsity provides a way around the “curse of dimensionality”.

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