A new approach for diagnosability analysis of Petri nets using Verifier Nets

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 fixed bound of K event occurrences after the fault. We give necessary and sufficient 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 Verifier 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 first time that necessary and sufficient conditions for diagnosability and diagnosability in K steps of labeled unbounded Petri nets are presented

Diagnosability of discrete event systems using labeled Petri nets

In this paper, we focus on labeled Petri nets with silent transitions that may either correspond to fault events or to regular unobservable events. We address the problem of deriving a procedure to determine if a given net system is diagnosable, i.e., the occurrence of a fault event may be detected for sure after a finite observation. The proposed procedure is based on our previous results on the diagnosis of discrete-event systems modeled with labeled Petri nets, whose key notions are those of basis markings and minimal explanations, and is inspired by the diagnosability approach for finite state automata proposed by Sampath in 1995. In particular, we first give necessary and sufficient conditions for diagnosability. Then, we present a method to test diagnosability that is based on the analysis of two graphs that depend on the structure of the net, including the faults model, and the initial marking

Basis Coverability Graph for Partially Observable Petri Nets with Application to Diagnosability Analysis

International audiencePetri nets have been proposed as a fundamental model for discrete-event systems in a wide variety of applications and have been an asset to reduce the computational complexity involved in solving a series of problems, such as control, state estimation, fault diagnosis, etc. Many of those problems require an analysis of the reachability graph of the Petri net. The basis reachability graph is a condensed version of the reachability graph that was introduced to efficiently solve problems linked to partial observation. It was in particular used for diagnosis which consists in deciding whether some fault events occurred or not in the system, given partial observations on the run of the system. However this method is, with very specific exceptions, limited to bounded Petri nets. In this paper, we introduce the notion of basis coverability graph to remove this requirement. We then establish the relationship between the coverability graph and the basis coverability graph. Finally, we focus on the diagnosability and stochastic diagnosability problems: we show how the basis coverability graph can be used to get efficient algorithms when such problems are decidable

Structural analysis of Petri nets

This chapter, that can be seen as the continuation of the previous one, presents additional background material on Petri nets. In particular, the main focus is on structural analysis, i.e., algebraic tools that do not require the enumeration of the reachability set of a marked net but are based on the analysis of the state equation, on the incidence matrix, etc. Meaningful structural properties, i.e., properties that are only related to the structure of the net and not to its initial marking, are also defined and analyzed. Subclasses of Petri nets are finally defined and simplified analysis criteria that pertain to these classes are presented

Probabilistic marking estimation in labeled petri nets

Given a labeled Petri net, possibly with silent (unobservable) transitions, we are interested in performing marking estimation in a probabilistic setting. We assume a known initial marking or a known finite set of initial markings, each with some a prioriprobability, and our goal is to obtain the conditional probabilities of possible markings of the Petri net, conditioned on an observed sequence of labels. Under the assumptions that (i) the set of possible markings, starting from any reachable marking and following any arbitrarily long sequence of unobservable transitions, is bounded, and (ii) a characterization of the a priori probabilities of occurrence for each transition enabled at each reachable marking is available, explicitly or implicitly, we develop a recursive algorithm that efficiently performs current marking estimation

Introduction to Petri nets

Petri nets are one of the most important discrete event systems formalisms. Three are the main reasons of this. Firstly, they provide a rich family of both logic and timed models, that share a set of formal tools. Secondly, they can be used in all phases of design of a control system. Finally, Petri nets have been successfully used in several research domains, such as max-plus algebra, markovian processes, supervisory control, etc. In this chapter we provide the basic notations and results in this framework, only focusing on a purely logic model called place/transition net

Marking observer in labeled petri nets with application to supervisory control

In this paper, we consider the problem of marking estimation in labeled Petri nets whose initial marking is known to belong to a given convex set, in the presence of silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). First, we demonstrate that all sets of markings consistent with a given sequence of observations can be described in linear algebraic terms (as a union of convex sets); subsequently, this observation is used to construct (offline) a marking observer under appropriate boundedness assumptions. Using the marking observer we show how to derive, at design time, a state feedback control law under the assumption that all transitions sharing a label can be enabled or disabled simultaneously as a group; this way, the most burdensome part of the computations is performed offline

State feedback control of labeled Petri nets with uncertainty in the initial marking

In this paper we consider the problem of designing a state feedback controller for a labeled Petri net whose initial marking is known to belong to a given convex set. We allow for silent transitions (i.e., transitions labeled with the empty word) and indistinguishable transitions (i.e., transitions sharing the same label with other transitions). Transitions that are neither silent nor indistinguishable, are said to be observable since the observation of their label univocally identifies them. Moreover, we divide the set of observable transitions into controllable and uncontrollable (all unobservable transitions are obviously uncontrollable). Based on our previous results on marking observation in the above setting, we show how to derive, at design time, a state feedback control law; this way, the most burdensome part of the computations, is performed off-line

Diagnosability analysis of an ABS system modeled using Petri nets

We consider the braking system of a vehicle equipped with an ABS. In a previous paper we presented a Petri net model of such a device assuming that the sensor that activates the ABS can be affected by a stuck-at-on fault. Here, the case in which the ABS sensor can be affected by both a stuck-at-on and a stuck-at-off fault is considered. Firstly, we consider the case in which the braking subsystems of different wheels cannot exchange information neither between them, nor with a coordinator. We show that in this local setting, where diagnosis is performed independently at each wheel, faults are not diagnosable. Secondly, we show that in a centralized setting, where the diagnoser can monitor each single wheel, the overall system is diagnosable. Finally, we assume that the braking systems of two wheels on the same side of the vehicle can exchange information and propose a communication protocol that makes the overall system diagnosable assuming both wheels are always in the same grip condition