An occupation kernel approach to optimal control

TL;DR

This paper introduces a new operator theoretic framework using occupation kernels in RKHSs to solve optimal control problems data-drivenly, enabling linear programming approaches in infinite-dimensional spaces.

Contribution

It develops a novel occupation kernel method that embeds trajectory data into RKHSs and links it with Liouville operators for solving optimal control problems.

Findings

Framework effectively embeds trajectory data in RKHSs.

Lifts nonlinear control problems into linear programs in infinite-dimensional spaces.

Demonstrates potential for data-driven optimal control solutions.

Abstract

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.