# Approximation of reachable sets using optimal control and support vector machines

arXiv: https://arxiv.org/abs/1412.3302 · HTML: https://mlsanity.com/paper/1412.3302/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Dec 2014.

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

- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning](https://mlsanity.com/paper/2209.08073/) (2022)

## Abstract (arXiv)

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of a function chosen in a reproducing kernel Hilbert space. In some sense, the method can be considered as an extension to the optimal control algorithm approach recently developed by Baier, Gerdts and Xausa. The convergence of the method is illustrated numerically for several examples.