Compositional Construction of Safety Controllers for Networks of Continuous-Space POMDPs

In this article, we propose a compositional framework for the synthesis of safety controllers for networks of partially observable discrete-time stochastic control systems (also known as continuous-space partially observable Markov decision processes (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 derive sufficient small-gain-type conditions in order to compositionally construct control barrier functions for interconnected POMDPs using local barrier functions computed for subsystems. The constructed control barrier functions for the overall networks 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.