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]