# Control Occupation Kernel Regression for Nonlinear Control-Affine Systems

arXiv: https://arxiv.org/abs/2106.00103 · HTML: https://mlsanity.com/paper/2106.00103/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 31 May 2021.

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

- [The Occupation Kernel Method for Nonlinear System Identification](https://mlsanity.com/paper/1909.11792/) (2019)
- [Technical Report: Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures](https://mlsanity.com/paper/1305.7484/) (2013)
- [Dynamic Mode Decomposition with Control Liouville Operators](https://mlsanity.com/paper/2101.02620/) (2021)
- [Motion Tomography via Occupation Kernels](https://mlsanity.com/paper/2101.02677/) (2021)
- [Controller design and value function approximation for nonlinear dynamical systems](https://mlsanity.com/paper/1503.06650/) (2015)

## Abstract (arXiv)

This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in vector-valued reproducing kernel Hilbert space (vvRKHS). The trajectories are embedded as the so-called higher order control occupation kernels which represent an operator on the vvRKHS corresponding to iterated integration after multiplication by a given controller. The solution to the system identification problem is then the unique solution of an infinite dimensional regularized regression problem. The representer theorem is then used to express the solution as finite linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem. The vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the developed approach.