Centralized and decentralized supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets

Abstract

Supervisory controller design to enforce boundedness, liveness, and reversibility in Petri nets is considered. The Petri nets considered may have non-unity weight arcs and both controllable and uncontrollable transitions. Algorithms for a centralized controller design approach are first developed. The developed algorithms always find a controller whenever it exists. This controller enforces boundedness, liveness, and reversibility; it also avoids deadlock. Furthermore, it is shown that the controller obtained is the least restrictive controller among all controllers which enforce desired properties. A decentralized controller design approach, based on overlapping decompositions, is then introduced. Algorithms to design decentralized controllers based on this approach are also developed. These controllers, when they exist, also guarantees boundedness, liveness, reversibility and deadlock freeness. The decentralized controllers have two main advantages over the centralized ones. First, they have reduced on-line computation and communication requirements. Second, the computational time required to design decentralized controllers is considerably less than that required for centralized controllers.