Decentralized controller design to enforce boundedness, liveness, and reversibility in Petri nets

Decentralized supervisory controller design based on overlapping decompositions to enforce boundedness, liveness, and reversibility is considerered for ordinary Petri nets with weighted arcs. In the proposed approach, the given Petri net is first decomposed into a number of overlapping Petri subnets and then expanded such that each Petri subnet appear as disjoint. A controller for each disjoint Petri subnet is next designed to enforce boundedness, liveness, and reversibility in that Petri subnet. Since each subnet is smaller than the original Petri net, this step is, in general, much easier than obtaining a centralized controller for the original Petri net. These controllers are then combined to obtain a controller for the expanded Petri net. Finally, the controller for the expanded Petri net is contracted to obtain a controller for the original Petri net. It is shown that this final controller enforces boundedness, liveness, and reversibility in the original Petri net.