Disjunctive normal formula based supervisory control policy for general Petri nets
Deverakonda, Vijayalakshmi
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https://hdl.handle.net/2142/50715
Description
Title
Disjunctive normal formula based supervisory control policy for general Petri nets
Author(s)
Deverakonda, Vijayalakshmi
Issue Date
2014-09-16
Director of Research (if dissertation) or Advisor (if thesis)
Sreenivas, Ramavarapu S.
Department of Study
Industrial&Enterprise Sys Eng
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Petri Nets
Abstract
A Petri net (PN) is said to be live if it is possible to re any transition, although not
immediately, from every reachable marking. A liveness enforcing supervisory policy (LESP)
determines which controllable transition is to be prevented from ring at a marking, to
ensure the supervised Petri net (PN) is live.
A LESP is said to be minimally restrictive if the following property is true { if a minimally
restrictive LESP prevents the ring of a transition at a marking, then all other LESPs should
do the same.
We restrict our attention to a class of general Petri nets (PN) structures, where the
existence of an LESP for an instance initialized at a marking, implies the existence of an
LESP when the same instance is initialized with a larger initial marking. We show that the
minimally restrictive LESP for an instance N from this class is characterized by a collection of
boolean formulae f tc(N)gtc2Tc , where Tc is the set of controllable transitions in the PN. The
literals in tc(N) are true if and only if the token-load of speci c places meet a threshold.
Consequently, appropriately placed threshold-sensors, which detect if the token-load of a
place is greater than or equal to a predetermined threshold, provide su cient information
to implement the minimally restrictive LESP.
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