Comparing Forward and Backward Reachability as Tools for Safety Analysis

摘要

Using only the existence and uniqueness of trajectories for a generic dynamic system with inputs, we define and examine eight types of forward and backward reachability constructs. If the input is treated in a worst-case fashion, any forward or backward reach set or tube can be used for safety analysis, but if the input is treated in a best-case fash-ion only the backward reach tube always provides the correct results. Fortunately, forward and backward algorithms can be exchanged if well-posed reverse time trajectories can be defined. Unfortunately, backward reachability constructs are more likely to suffer from numerical stabil-ity issues, especially in systems with significant contraction—the very systems where forward simulation and reachability are most effective.