On Supervisory Policies That Enforce Liveness in a Class of Completely Controlled Petri Nets Obtaine - Automatic Control, IEEE Transactions on

نویسنده

  • Ramavarapu S. Sreenivas
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.

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تاریخ انتشار 1999