  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.
