Synthesis of Stochastic Systems with Partial Information via Control Barrier Functions ⁎⁎This work was supported in part by the H2020 ERC Starting Grant AutoCPS, the German Research Foundation (DFG) through the grants ZA 873/1-1 and the Research Training Group 2428, and the TUM International Graduate School of Science and Engineering (IGSSE). †The authors contributed equally to this work.

Synthesis of controllers for stochastic control systems ensuring safety constraints has gained considerable attention in the last few years. In this paper, we consider the problem of synthesizing controllers for partially observed stochastic control systems to ensure finite-time safety. Given an estimator with a probabilistic guarantee on the accuracy of the estimations, we provide an approach to compute a controller providing a lower bound on the probability that the trajectories of the stochastic control system remain safe over a finite time-horizon. To obtain such controllers, we utilize a notion of control barrier functions. We also provide an approach to compute a probability bound on estimator accuracy by using a notion of so-called stochastic simulation function. The proposed result is illustrated on a case study.