  In this paper, we propose a compositional framework for the synthesis of
safety controllers for networks of partially-observed discrete-time stochastic
control systems (a.k.a. continuous-space POMDPs). Given an estimator, we
utilize a discretization-free approach to synthesize controllers ensuring
safety specifications over finite-time horizons. The proposed framework is
based on a notion of so-called local control barrier functions computed for
subsystems in two different ways. In the first scheme, no prior knowledge of
estimation accuracy is needed. The second framework utilizes a probability
bound on the estimation accuracy using a notion of so called stochastic
simulation functions. In both proposed schemes, we drive sufficient small-gain
type conditions in order to compositionally construct control barrier functions
for interconnected POMDPs using local barrier functions computed for
subsystems. Leveraging compositionality results, the constructed control
barrier functions enable us to compute lower bounds on the probabilities that
the interconnected POMDPs avoid certain unsafe regions in finite-time horizons.
We demonstrate the effectiveness of our proposed approaches by applying them to
an adaptive cruise control problem.
