Petri net supervisors for DES with uncontrollable and unobservable transitions

A supervisor synthesis technique for Petri net plants with uncontrollable a nd unobservable transitions that enforces the conjunction of a set of linea r inequalities on the reachable markings of the plant is presented. The app roach is based on the concept of Petri net place invariants. Each step of t he procedure is illustrated through a running example involving the supervi sion of a robotic assembly cell. The controller is described by an auxiliar y Petri net connected to the plant's transitions, providing a unified Petri net model of the closed-loop system, The synthesis technique is based on t he concept of admissible constraints. An inadmissible constraint cannot be directly enforced on a plant because of the uncontrollability or unobservab ility of certain plant transitions. Procedures are given for identifying al l admissible linear constraints for a plant with uncontrollable and unobser vable transitions, as well as methods for transforming inadmissible constra ints into admissible ones, When multiple transformations of this kind occur , a technique is described for creating a modified Petri net controller tha t enforces the union of all of these control laws. The method is practical and computationally inexpensive in terms of size, design time, and implemen tation complexity.