Petri Net Supervisors for DES with Uncontrollable and Unobservable Transitions

J.O. Moody and P.J. Antsaklis

IEEE Trans. Automatic Control, Vol. 45, No. 3, pp. 462-476, March 2000.

Abstract -- A supervisor synthesis technique for Petri net plants with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the reachable markings of the plant is presented. The approach is based on the concept of petri net place invariants. Each step of the procedure is illustrated through a running example involving the supervision of a robotic assembly cell. The controller is described by an auxiliary Petri net connected to the plant's transitions, providing a unified Petri net model of the closed loop system. The systhesis technique is based on the concept of admissible constraints. An inadmissible constraint can not be directly enforced on a plant due to the uncontrollability or unobservability of certain plant transitions. Procedures are given for identifying all admissible linear constraints for a plant with uncontrollable and unobservable transitions, as well as methods for transforming inadmissible constraints into admissible ones. When there are multiple transformations of this kind, a technique is described for creating a modified Petri net controller that enforces the union of all these control laws. It is shown how a variety of supervisory control problems can be formulated and solved using the method proposed here. The method is practical and computationally inexpensive in terms of size, design time, and implementation complexity.

Journal Submission [pdf file]


Also appeared as Technical Report isis-99-004, Department of Electrical Engineering, University of Notre Dame, Feb. 1999.

Technical Report [postscript file] [pdf file]