Reach-avoid Analysis for Stochastic Discrete-time Systems

Bai Xue, Renjue Li, Naijun Zhan, Martin Fränzle
2021 American Control Conference (ACC)
Stochastic discrete-time systems, i.e., discrete-time dynamic systems subject to stochastic disturbances, are an essential modelling tool for many engineering systems, and reach-avoid analysis is able to guarantee safety (i.e., via avoiding unsafe sets) and progress (i.e., via reaching target sets). In this paper we study the reach-avoid problem of stochastic discrete-time systems over open (i.e., not bounded a priori) time horizons. The stochastic discrete-time system of interest is modeled by iterative polynomial maps with stochastic disturbances, and the problem addressed is to effectively compute an inner approximation of its p-reach-avoid set. The p-reach-avoid set collects those initial states that give rise to a bundle of trajectories which with probability being larger than p eventually hits a designated set of target states while remaining inside a set of safe states before the first hit. The computation of the p-reach-avoid …
05 / 2021