# Data-driven optimal control of unknown nonlinear dynamical systems using the Koopman operator

arXiv: https://arxiv.org/abs/2412.01085 · HTML: https://mlsanity.com/paper/2412.01085/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Dec 2024.

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

- [Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansion](https://mlsanity.com/paper/2506.01356/) (2025)
- [Koopman Dreamer: Spectrally Constrained Latent Dynamics for Stable World-Model Imagination](https://mlsanity.com/paper/2607.19719/) (2026)

## Abstract (arXiv)

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings. This work develops a theoretically certifiable framework that integrates a modified Koopman operator approach with model-based reinforcement learning to address these challenges. By relaxing the requirements on observable functions, our method incorporates nonlinear terms involving both states and control inputs, significantly enhancing system identification accuracy. Moreover, by leveraging the power of neural networks to solve partial differential equations (PDEs), our approach is able to achieving stabilizing control for high-dimensional dynamical systems, up to 9-dimensional. The learned value function and control laws are proven to converge to those of the true system at each iteration. Additionally, the accumulated cost of the learned control closely approximates that of the true system, with errors ranging from 10-5 to 10-3.