Controlled Timed Petri Nets: Equivalence Relations, Model Reduction

Discusses controlled timed Petri net models for the formal synthesis of supervisory controllers for real time discrete event systems (e.g. communication protocols, supervisors for FMSs, control of batch processes). We extend the standard Petri net formalism with firing delays between the time a transition becomes state enabled, and the time it is executed. These firing delays are partly controllable between lower and upper bounds. The goal is to guarantee that certain forbidden distributions of tokens will never occur. For this purpose we define the influencing net corresponding to forbidden sets. Deciding whether a maximally permissive controller exists, and if yes, constructing such a controller, requires solving large sets of linear inequalities over firing times in this influencing net. This is generally a very large set. Hence we study some equivalence relations between different subnets of a timed Petri net. An example shows that replacing a subnet by a simpler equivalent subnet can significantly reduce the size of the sets of inequalities to be solved.