Petri net supervisors for discrete event systems
John O. Moody, Panos J. Antsaklis · 1998
Supervisory control is the process of limiting the actions of a plant, normally described as a discrete event system (DES), to a set of safe, allowable, or desirable behaviors. DES models may have an application-specific specialized form, but are generally described as automata or Petri nets. The benefits of Petri net models over automata include the handling of concurrent events, a more compact representation of a larger reachable state space, and increased complexity of possible system behaviors. A method is developed here for enforcing logical intersections and unions of linear predicates on the reachable state space of a Petri net plant. The control computation, based on the well understood concept of Petri net place invariants, is straight forward and computationally inexpensive. The resulting feedback controller is itself a Petri net, providing a unified plant/controller model description that facilitates analysis, simulation, verification, and implementation. The most difficult problems in supervisory control involve designing controllers when certain events in the plant can not be inhibited or can not be sensed by an observer. The theoretical implications of uncontrollable and unobservable transitions are explored here in light of invariant based controllers. Computational techniques are developed for generating control laws and supervisors as well as means of characterizing all feasible Petri net controllers under these conditions. The practical utility of the constraints that these invariant based controllers can realize is thoroughly explored. The method is shown to be useful for enforcing a wide range of forbidden state problems, handling the allocation and use of finite resources, avoiding deadlock and insuring liveness, enforcing direct and indirect conditions on allowable plant events, realizing logical predicates on plant behavior, and handling constraints involving real time. Examples are provides throughout the text to illustrate and motivate the various control techniques and applications. Larger examples that incorporate the use of multiple techniques are collected at the end of the dissertation.