Computing bounds for forbidden state reachability functions for controlled Petri nets

Characterizing uncontrollable reachability is a central issue in forbidden state control of discrete event systems. In this paper, we present methods for building expressions which estimate uncontrollable reachability in a general class of Petri nets and which characterize the control sets to ensure future markings will not be forbidden. These expressions are determined by constructing an abstract syntax tree from an analysis of the Petri net model of the system. We show that these expressions represent bounds that are useful for evaluating uncontrollable reachability and for evaluating control actions.