Backward Reachability of Autonomous Max-Plus-Linear Systems

This work discusses the backward reachability of autonomous Max-Plus-Linear (MPL) systems, a class of continuous-space discrete-event models that are relevant for applications dealing with synchronization and scheduling. Given an MPL system and a continuous set of final states, we characterize and compute its “backward reach tube” and “backward reach sets, ” namely the set of states that can reach the final set within a given event interval or at a fixed event step, respectively. We show that, in both cases, the computation can be done exactly via manipulations of difference-bound matrices. Furthermore, we illustrate the application of the backward reachability computations over safety and transient analysis of MPL systems.