Conservative Safety Monitors of Stochastic Dynamical Systems

Abstract: Generating accurate runtime safety estimates for autonomous systems is vital to ensuring their continued proliferation. However, exhaustive reasoning about future behaviors is generally too complex to do at runtime. To provide scalable and formal safety estimates, we propose a method for leveraging design-time model checking results at runtime. Specifically, we model the system as a probabilistic automaton (PA) and compute bounded-time reachability probabilities over the states of the PA at design time. At runtime, we combine distributions of state estimates with the model checking results to produce a bounded time safety estimate. We argue that our approach produces well-calibrated safety probabilities, assuming the estimated state distributions are well-calibrated. We evaluate our approach on simulated water tanks.