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.

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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.

A system is said to be opaque if a given secret behavior remains opaque (uncertain) to an intruder who can partially observe system activities. This work addresses the verification of state-based opacity in systems modeled with Petri nets. The secret behavior of a system is defined as a set of states. More precisely, two state-based opacity properties are considered: current-state opacity and initial-state opacity. We show that both current-state and initial-state opacity problems in bounded Petri nets can be efficiently solved by using a compact representation of the reachability graph, called basis reachability graph (BRG). This approach is practically efficient since the exhaustive enumeration of the reachability space can be avoided.

In this paper we analyze the diagnosability properties of labeled Petri nets. We consider the standard notion of diagnosability of languages, requiring that every occurrence of an unobservable fault event be eventually detected, as well as the stronger notion of diagnosability in K steps, where the detection must occur within a xed bound of K event occurrences after the fault. We give necessary and sucient conditions for these two notions of diagnosability for both bounded and unbounded Petri nets and then present an algorithmic technique for testing the conditions based on linear programming. Our approach is novel and based on the analysis of the reachability/coverability graph of a special Petri net, called Verier Net, that is built from the Petri net model of the given system. In the case of systems that are diagnosable in K steps, we give a procedure to compute the bound K. To the best of our knowledge, this is the rst time that necessary and sucient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented.