Probabilistic Sequential Safety for Stochastic Dynamical Systems

Abstract

In this letter, we investigate a notion of probabilistic safety for a stochastic dynamical system. Standard safety notions are based on the idea that an unsafe region of the state-space must be avoided at each instant. In contrast, we study a sequential safety notion which is based on avoiding a tuple of target regions of the state-space. The proposed safety notion is inspired by many practical systems, ranging from modeling jailbreak attacks in large language models (LLMs) to predicting hazardous chemical reactions. In solving the sequential safety problem, we solve a sequential reachability problem for a stochastic dynamical system.