Summary: 1962 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 48, NO. 11, NOVEMBER 2003
Design of -Liveness Enforcing
Supervisors in Petri Nets
Marian V. Iordache, Student Member, IEEE, and Panos J. Antsaklis, Fellow, IEEE
Abstract--This paper presents a procedure for the design of
supervisors that enforce the transitions in a given set to be live.
-liveness enforcement corresponds to full liveness enforcement
when equals the total set of transitions. Rather than assuming a
given initial marking, this procedure generates at every iteration
a convex set of admissible initial markings. In the case of full
liveness enforcement and under certain conditions also in the case
of -liveness enforcement, the convex set of each iteration includes
the set of markings for which liveness/ -liveness can be enforced.
When the procedure terminates, and if it terminates, the final
convex set contains only markings for which -liveness can be
enforced. Then, the supervisor keeping the Petri net (PN) marking
in this convex set can be easily designed using the place invariant
based approach. This paper focuses on the fully controllable and
observable PNs. Several extensions of the procedure, including to
partially controllable and observable PNs, are outlined.