# An occupation kernel approach to optimal control

arXiv: https://arxiv.org/abs/2106.00663 · HTML: https://mlsanity.com/paper/2106.00663/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2021.

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

- [Stochastic Nonlinear Control via Finite-dimensional Spectral Dynamic Embedding](https://mlsanity.com/paper/2304.03907/) (2023)

## Abstract (arXiv)

In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the resolution of optimal control problems in dynamical systems. Trajectory information in the dynamical systems is embedded in a reproducing kernel Hilbert space (RKHS) through what are called occupation kernels. The occupation kernels are tied to the dynamics of the system through the densely defined Liouville operator. The pairing of Liouville operators and occupation kernels allows for lifting of nonlinear finite-dimensional optimal control problems into the space of infinite-dimensional linear programs over RKHSs.