AbstmctWe study a class of specifications, called generalized mutual exclusion constraints, for discrete event systems modeled using Placellkansition nets. These specifications may be easily enforced by a set of places called monitors on a net system where all transitions are controllable. However, when some of the transitions of the net are uncontrollable this technique is not always applicable. For some classes of nets, we prove that generalized mutual exclusion constraints may always be enforced by monitors, even in the presence of uncontrollable transitions.
In this paper we present a fault detection approach for discrete event systems using Petri nets. We assume that some of the transitions of the net are unobservable, including all those transitions that model faulty behaviors. Our diagnosis approach is based on the notions of basis marking and justification, that allow us to characterize the set of markings that are consistent with the actual observation, and the set of unobservable transitions whose firing enable it. This approach applies to all net systems whose unobservable subnet is acyclic. If the net system is also bounded the proposed approach may be significantly simplified by moving the most burdensome part of the procedure off-line, thanks to the construction of a graph, called the basis reachability graph.
In this paper we discuss the problem of estimating the marking of a Place/Transition net based on event observation. We assume that the net structure is known while the initial marking is totally or partially unknown. We give algorithms to compute a marking estimate that is a lower bound of the actual marking. The special structure of Petri nets allows us to use a simple linear algebraic formalism for estimate and error computation. The error between actual marking and estimate is a monotonically non-increasing function of the observed word length, and words that lead to null error are said complete. We define several observability properties related to the existence of complete words, and show how they can be proved. To prove some of them we also introduce a useful tool, the observer coverability graph, i.e., the usual coverability graph of a Place/Transition net augmented with a vector that keeps track of the estimation error on each place of the net. Finally, we show how the estimate generated by the observer may be used to design a state feedback controller for forbidden marking specifications.
Abstract-We consider in this paper first-order hybrid Petri Nets, a model that consists of continuous places holding fluid, discrete places containing a nonnegative integer number of tokens, and transitions, either discrete or continuous. We set up a linear algebraic formalism to study the first-order continuous behavior of this model and show how its control can be framed as a conflict resolution policy that aims at optimizing a given objective function. The use of linear algebra leads to sensitivity analysis that allows one to study of how changes in the structure of the model influence the optimal behavior. As an example of application, we show how the proposed formalism can be applied to flexible manufacturing systems with arbitrary layout and different classes of products.
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