Finite-time Safety and Reach-avoid Verification of Stochastic Discrete-time Systems

TL;DR

This paper develops new probabilistic verification methods for assessing safety and reach-avoid properties of stochastic discrete-time systems within finite time horizons, using barrier-like conditions.

Contribution

It introduces novel barrier-like conditions for finite-time safety and reach-avoid verification, filling gaps in existing methods for stochastic systems.

Findings

Effective bounds demonstrated on example systems

Barrier conditions complement existing verification techniques

Applicable to a range of stochastic discrete-time models

Abstract

This paper studies finite-time safety and reach-avoid verification for stochastic discrete-time dynamical systems. The aim is to ascertain lower and upper bounds of the probability that, within a predefined finite-time horizon, a system starting from an initial state in a safe set will either exit the safe set (safety verification) or reach a target set while remaining within the safe set until the first encounter with the target (reach-avoid verification). We introduce novel barrier-like sufficient conditions for characterizing these bounds, which either complement existing ones or fill gaps. Finally, we demonstrate the efficacy of these conditions on two examples.