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Summary: IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 18, NO. 1, FEBRUARY 2002 59
Synthesis of Deadlock Prevention Supervisors
Using Petri Nets
Marian V. Iordache, John O. Moody, Member, IEEE, and Panos J. Antsaklis, Fellow, IEEE
Abstract--Given an arbitrary Petri net (PN) structure, which
may have uncontrollable and unobservable transitions, the dead-
lock prevention procedure presented here determines a set of linear
inequalities on the PN markings. When the PN is supervised so that
its markings satisfy these inequalities, the supervised net is proved
to be deadlock-free for all initial markings that satisfy the supervi-
sion constraints. Deadlock-freedom implies that there will always
be at least one transition that is enabled in the closed-loop (super-
vised) system. The method is not guaranteed to ensure liveness, as
it can be applied to systems that cannot be made live under any
circumstances. However, for controllable and observable PNs, it
is shown that, when the method ensures liveness as well, the live-
ness-ensuring supervisor is least restrictive. Moreover, it is shown
that the method is not restrictive even for PNs in which not all tran-
sitions can be made live. The procedure allows automated synthesis
of the supervisors.
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