We consider discrete-state plants represented by controlled Petri nets (CtIPN's), where a subset of transitions can be prevented from firing by a super visor. A transition in a CtIPN can fire at a marking if there are sufficient tokens in its input places and it is permitted to fire by the supervisor. A CtIPN is live if it is possible to fire any transition from every marking that is reachable under supervision. In this paper we derive a necessary and sufficient condition for the existence of a supervisory policy that enforces liveness in CtIPN's. We show this condition cannot be tested for an arbitrary CtIPN. However, for bounded CtIPN's, or CtIPN's where each transition is individually controllable, we show the existence of a supervisory policy which enforces that livenessisdecidable. We also show the existence of a supervisory policy that enforces liveness is necessary and sufficient for the existence of a minimally restrictive supervisory policy.
- Petri nets
- Supervisory control
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering