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.
Cite
@article{arxiv.1908.00697,
title = {Model-Free Stochastic Reachability Using Kernel Distribution Embeddings},
author = {Adam J. Thorpe and Meeko M. K. Oishi},
journal= {arXiv preprint arXiv:1908.00697},
year = {2020}
}