Abstract
The existence of a supervisory policy that enforces liveness in partially controlled Petri nets (PNs) is undecidable in general (cf. theorem 5.3 and corollary 5.2). However, there can be families of partially controlled PNs for which the existence of a supervisory policy that enforces liveness can be tested and synthesized. In this paper we present choice-controlled PNs as an example of such a family. Also, there can be specific examples of partially controlled PNs that be made live by supervision. Typically, this is shown by producing a supervisory policy that enforces liveness in the example at hand. There can be no generalization of this approach in light of theorem 5.3 and corollary 5.2 in reference [9]. However, for partially controlled Free-Choice PNs, there is a necessary and sufficient characterization of supervisory policies that enforce liveness. In specific, the necessary and sufficient condition for the existence of a supervisory policy that enforces liveness in a fully controlled Free-Choice Petri Net (FCPN) in reference [8] also holds for partially controlled FCPNs. This condition can be used to verify that a given supervisory policy does enforce liveness in a specific partially controlled FCPN.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3730-3734 |
| Number of pages | 5 |
| Journal | Proceedings of the IEEE Conference on Decision and Control |
| Volume | 4 |
| State | Published - 2003 |
| Event | 42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: Dec 9 2003 → Dec 12 2003 |
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization