  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.
