This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.
This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We provide an algorithm to construct a novel structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer linear programming problems (ILPPs). For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an efficient approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require exhaustive exploration of the state space and therefore achieves significant practical efficiency, as shown by means of numerical simulations.
For an automated manufacturing system (AMS), it is a computationally intractable problem to find a maximally permissive deadlock avoidance policy (DAP) in a general case, since the decision on the safety of a reachable state is NP-hard. This paper focuses on the deadlock avoidance problem for systems of simple sequential processes with resources (S 3 PR) by using Petri nets structural analysis theory. Inspired by the one-step look-ahead DAP that is an established result, which is of polynomial complexity, for an S 3 PR without one-unit-capacity resources shared by two or more resource-transition circuits (in the Petri net model) that do not include each other, this research explores a multiple-step look-ahead deadlock avoidance policy for a system modeled with an S 3 PR that contains a shared one-unit-capacity resource in resource-transition circuits. It is shown that the development of an optimal DAP for the considered class of Petri nets is also of polynomial complexity. It is indicated that the steps needed to look ahead in a DAP depend on the structure of the net model. A number of examples are used to illustrate the proposed method.
This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimal-maximal basis reachability graph (min-max-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its min-max-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the min-max-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of dead markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the min-max-BRG.The approach we developed does not require the construction of the reachability graph and has wide applicability.
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