Safe & Robust Reachability Analysis of Hybrid Systems
For researchers in hybrid systems verification, this work addresses foundational safety and robustness issues in reachability analysis, though it remains theoretical without empirical validation.
The paper identifies that standard reachability definitions for hybrid systems can be unsafe (computing a proper subset of reachable states) and proposes 'safe reachability' which computes a superset. It also shows that the best Scott continuous approximation of an analysis is its best robust approximation under certain conditions, and demonstrates the gap between reachable states and these supersets.
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of reachability - namely, the reflexive and transitive closure of a transition relation - can be unsafe, ie, it may compute a proper subset of the set of states reachable in finite time from a set of initial states. Therefore, we propose safe reachability, which always computes a superset of the set of reachable states. Second, in safety analysis of hybrid and continuous systems, it is important to ensure that a reachability analysis is also robust wrt small perturbations to the set of initial states and to the system itself, since discrepancies between a system and its mathematical models are unavoidable. We show that, under certain conditions, the best Scott continuous approximation of an analysis A is also its best robust approximation. Finally, we exemplify the gap between the set of reachable states and the supersets computed by safe reachability and its best robust approximation.