Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment does not evolve. Online, however, an autonomous system might experience changes in system dynamics, control authority, external disturbances, and/or the surrounding environment, requiring updated safety assurances. Rather than restarting the safety analysis from scratch, which can be time-consuming and often intractable to perform online, we propose to compute \textit{parameter-conditioned} reachable sets. Assuming expected system and environment changes can be parameterized, we treat these parameters as virtual states in the system and leverage recent advances in high-dimensional reachability analysis to solve the corresponding reachability problem offline. This results in a family of reachable sets that is parameterized by the environment and system factors. Online, as these factors change, the system can simply query the corresponding safety function from this family to ensure system safety, enabling a real-time update of the safety assurances. Through various simulation studies, we demonstrate the capability of our approach in maintaining system safety despite the system and environment evolution.

翻译：Hamilton-Jacobi（HJ）可达性分析是分析自主系统安全性的有力工具。然而，所提供的安全保证通常基于一个假设：系统一旦部署，其自身或所处环境将不再演化。但在线情况下，自主系统可能经历系统动力学、控制权限、外部扰动和/或周围环境的变化，这要求安全保证能够随之更新。为了避免从头重启安全分析（这既耗时又往往难以在线实现），我们提出计算**参数条件化的**可达集。假设预期的系统与环境变化可参数化，我们将这些参数视为系统中的虚拟状态，并利用高维可达性分析的最新进展，离线求解相应的可达性问题。由此得到一系列由环境与系统因子参数化的可达集。在线情况下，随着这些因子变化，系统可直接从该族集中查询对应的安全函数，从而确保系统安全，实现安全保证的实时更新。通过多项仿真研究，我们证明了该方法在系统与环境演化过程中维持系统安全性的能力。