On Supervisory Policies That Enforce Liveness in a Class of Completely Controlled Petri Nets Obtaine - Automatic Control, IEEE Transactions on
نویسنده
چکیده
The authors consider Petri nets (PN’s) [3], where each transition can be prevented from firing by an external agent, the supervisor. References [5] and [6] contain necessary and sufficient conditions for the existence of a supervisory policy that enforces liveness in a PN that is not live. A PN is said to be live if it is possible to fire any transition from every reachable marking, although not necessarily immediately. The procedure in [5] and [6] involves the construction of the coverability graph (cf. [3, Sec. 5.1]), which can be computationally expensive. Using the refinement/abstraction procedure of Suzuki and Murata [8], where a single transition in a abstracted PN N is replaced by a PN ~ N to yield a larger refined PN ^ N , we show that when ~ N belongs to a class of markedgraph PN’s (cf. [3, Sec. 6.1]), there is a supervisory policy that enforces liveness in the refined PN ^ N if and only if there is a similar policy for the abstracted PN N . Since the coverability graph of the PN N is smaller than that of the PN ^ N , it is possible to achieve significant computational savings by using the process of abstraction on ^ N . This is illustrated by example.
منابع مشابه
Some observations on supervisory policies that enforce liveness in partially controlled Free-Choice Petri nets
Every arc from a place to a transition in a Free-Choice Petri net (FCPN) is either the unique output arc of the place, or, the unique input arc to the transition [M.H.T. Hack, Analysis of production schemata by Petri nets, Master’s thesis, Massachusetts Institute of Technology, February 1972; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and a...
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The process of synthesizing a supervisory policy that enforces liveness in a Petri net (PN) 4, 3] where each transition can be prevented from ring by an external agent, can be com-putationally burdensome in general 7]. In this paper we consider PNs that have a directed cut-place, or, a cut-transition. A place (transition) in a connected PN is said to be a cut-place (cut-transition) if its remov...
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On supervisory policies that enforce liveness in completely controlled petri nets with directed cut-places and cut-transitions. On supervisory policies that enforce liveness in in a class of completely controlled petri nets obtained via reenement. Starting from the observation that the set of initial markings (N) for which there is a supervisory policy that enforces liveness in a partially cont...
متن کاملOn Readily Available Supervisory Control Policies That Enforce Liveness in a Class of Completely Controlled Petri Nets
A Petri Net (PN) is said to be live if it is possible to re any transition from every reachable marking, although not necessarily immediately. Under appropriate conditions, a non-live PN can be made live via supervision. Under this paradigm an external-agent, the supervisor, prevents the ring of certain transitions at each reachable marking so as to enforce liveness. A PN is said to be complete...
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