# Model-Free Stochastic Reachability Using Kernel Distribution Embeddings

## TL;DR

This paper introduces a kernel-based, data-driven method for solving stochastic reachability problems in control processes, enabling efficient computation in high-dimensional systems without intractable integrals.

## Contribution

It presents a novel nonparametric approach using RKHS embeddings to handle stochastic kernels in reachability analysis, avoiding complex integrals.

## Key findings

- Effective in high-dimensional systems
- Reduces computational complexity
- Applicable to various dynamical models

## Abstract

We present a solution to the terminal-hitting stochastic reach-avoid problem for a Markov control process. This solution takes advantage of a nonparametric representation of the stochastic kernel as a conditional distribution embedding within a reproducing kernel Hilbert space (RKHS). Because the disturbance is modeled as a data-driven stochastic process, this representation avoids intractable integrals in the dynamic recursion of the reach-avoid problem since the expectations can be calculated as an inner product within the RKHS. We demonstrate this approach on a high-dimensional chain of integrators and on Clohessy-Wiltshire-Hill dynamics.