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

TL;DR

This paper introduces a compositional framework for designing safety controllers for networks of continuous-space POMDPs, enabling safety guarantees through local barrier functions without requiring discretization.

Contribution

It presents novel compositional methods for synthesizing safety controllers for interconnected POMDPs using local control barrier functions and small-gain conditions.

Findings

Successfully applied to an adaptive cruise control scenario.

Provides lower bounds on safety probabilities for interconnected systems.

No prior knowledge of estimation accuracy needed in one scheme.

Abstract

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.