  Reachability analysis of hybrid systems has been used as a safety
verification tool to assess offline whether the state of a system is capable of
remaining within a designated safe region for a given time horizon. Although it
has been applied to stochastic hybrid systems, little work has been done on the
equally important problem of reachability under incomplete or noisy
measurements of the state. Further, there are currently no computational
methods or results for reachability analysis of partially observable discrete
time stochastic hybrid systems. We provide the first numerical results for
solving this problem, by drawing upon existing literature on continuous state
partially observable Markov decision processes (POMDPs). We first prove that
the value function for the reachability problem (with a multiplicative cost
structure) is piecewise-linear and convex, just as for discrete state POMDPs
with an additive cost function. Because of these properties, we are able to
extend existing point-based value iteration techniques to the reachability
problem, demonstrating its applicability on a benchmark temperature regulation
problem.
