Diagnosability Analysis of Labeled Time Petri Net Systems

In this paper, we focus on two notions of diagnosability for labeled Time Petri net (PN) systems: K-diagnosability implies that any fault occurrence can be detected after at most K observations, while τ-diagnosability implies that any fault occurrence can be detected after at most τ time units. A procedure to analyze such properties isprovided.The proposedapproach uses the Modified State Class Graph, a graph the authors recently introduced for the marking estimation of labeled Time PN systems,which providesan exhaustive description of the system behavior. A preliminary diagnosabilty analysis of the underlying logic system based on classical approaches taken from the literature is required. Then, the solution of some linear programming problems should be performed to take into account the timing constraints associated with transitions

PetriBaR: A MATLAB Toolbox for Petri Nets Implementing Basis Reachability Approaches

This paper presents a MATLAB toolbox, called PetriBaR, for the analysis and control of Petri nets. PetriBaR is a package of functions devoted to basic Petri net analysis (including the computation of T-invariants, siphons, reachability graph, etc.), monitor design, reachability analysis, state estimation, fault diagnosis, and opacity verification. In particular, the functions for reachability analysis, state estimation, fault diagnosis, and opacity verification exploit the construction of the Basis Reachability Graph to avoid the exhaustive enumeration of the reachable set, thus leading to significant advantages in terms of computational complexity. All functions of PetriBaR are introduced in detail clarifying the syntax to be used to run them. Finally, they are illustrated via a series of numerical examples. PetriBaR is available online for public access

Une approche efficace pour l’étude de la diagnosticabilité et le diagnostic des SED modélisés par Réseaux de Petri labellisés : contextes atemporel et temporel

This PhD thesis deals with fault diagnosis of discrete event systems using Petri net models. Some on-the-fly and incremental techniques are developed to reduce the state explosion problem while analyzing diagnosability. In the untimed context, an algebraic representation for labeled Petri nets (LPNs) is developed for featuring system behavior. The diagnosability of LPN models is tackled by analyzing a series of K-diagnosability problems. Two models called respectively FM-graph and FM-set tree are developed and built on the fly to record the necessary information for diagnosability analysis. Finally, a diagnoser is derived from the FM-set tree for online diagnosis. In the timed context, time interval splitting techniques are developed in order to make it possible to generate a state representation of labeled time Petri net (LTPN) models, for which techniques from the untimed context can be used to analyze diagnosability. Based on this, necessary and sufficient conditions for the diagnosability of LTPN models are determined. Moreover, we provide the solution for the minimum delay ∆ that ensures diagnosability. From a practical point of view, diagnosability analysis is performed on the basis of on-the-fly building of a structure that we call ASG and which holds fault information about the LTPN states. Generally, using on-the-fly analysis and incremental technique makes it possible to build and investigate only a part of the state space, even in the case when the system is diagnosable. Simulation results obtained on some chosen benchmarks show the efficiency in terms of time and memory compared with the traditional approaches using state enumerationCette thèse s'intéresse à l'étude des problèmes de diagnostic des fautes sur les systèmes à événements discrets en utilisant les modèles réseau de Petri. Des techniques d'exploration incrémentale et à-la-volée sont développées pour combattre le problème de l'explosion de l'état lors de l'analyse de la diagnosticabilité. Dans le contexte atemporel, la diagnosticabilité de modèles RdP-L est abordée par l'analyse d'une série de problèmes K-diagnosticabilité. L'analyse de la diagnosticabilité est effectuée sur la base de deux modèles nommés respectivement FM-graph et FM-set tree qui sont développés à-la-volée. Un diagnostiqueur peut être dérivé à partir du FM-set tree pour le diagnostic en ligne. Dans le contexte temporel, les techniques de fractionnement des intervalles de temps sont élaborées pour développer représentation de l'espace d'état des RdP-LT pour laquelle des techniques d'analyse de la diagnosticabilité peuvent être utilisées. Sur cette base, les conditions nécessaires et suffisantes pour la diagnosticabilité de RdP-LT ont été déterminées. En pratique, l'analyse de la diagnosticabilité est effectuée sur la base de la construction à-la-volée d'une structure nommée ASG et qui contient des informations relatives à l'occurrence de fautes. D'une manière générale, l'analyse effectuée sur la base des techniques à-la-volée et incrémentale permet de construire et explorer seulement une partie de l'espace d'état, même lorsque le système est diagnosticable. Les résultats des simulations effectuées sur certains benchmarks montrent l'efficacité de ces techniques en termes de temps et de mémoire par rapport aux approches traditionnelles basées sur l'énumération des état

Generation of mathematical programming representations for discrete event simulation models of timed petri nets

This work proposes a mathematical programming (MP) representation of discrete event simulation of timed Petri nets (TPN). Currently, mathematical programming techniques are not widely applied to optimize discrete event systems due to the difficulty of formulating models capable to correctly represent the system dynamics. This work connects the two fruitful research fields, i.e., mathematical programming and Timed Petri Nets. In the MP formalism, the decision variables of the model correspond to the transition firing times and the markings of the TPN, whereas the constraints represent the state transition logic and temporal sequences among events. The MP model and a simulation run of the TPN are then totally equivalent, and this equivalence has been validated through an application in the queuing network field. Using a TPN model as input, the MP model can be routinely generated and used as a white box for further tasks such as sensitivity analysis, cut generation in optimization procedures, and proof of formal properties

Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties

Fourier-Motzkin methods for fault diagnosis in discrete event systems

The problem of fault diagnosis under partial observation is a complex problem; and the challenge to solve this problem is to find a compromise between the space complexity and time complexity. The classic method to solve the problem is by constructing an automaton called a diagnoser. This method suffers from the state explosion problem which limits its application to large systems. In this thesis, the problem of fault diagnosis in partially observed discrete event systems is addressed. We assume that the system is modelled by Petri nets having no cycle of unobservable transitions. The class of labelled Petri nets is also considered with both bounded and unbounded cases. We propose a novel approach for fault diagnosis using the Integer Fourier-Motzkin Elimination method. The main idea is to reduce the problem of constructing the diagnoser to a problem of projecting between two spaces. In other words, we first obtain a set of inequalities derived from the state equation of Petri nets. Then, the elimination method is used to drop the variables corresponding to the unobservable transitions and we design two sets of inequalities in variables representing the observable transitions. One set ensures that the fault has occurred, whereas the other ensures that fault has not occurred. Given these two sets, we have proved that the occurrences of faults can be decided as any other diagnoser can do. The obtained result are extended to diagnose violations of constraints such as service level agreement and Quality of Service, which is of particular interested in telecommunication companies. We implement our approach and demonstrate gains in performance with respect to existing approaches on a benchmark example

Twin‐engined diagnosis of discrete‐event systems

Diagnosis of discrete-event systems (DESs) is computationally complex. This is why a variety of knowledge compilation techniques have been proposed, the most notable of them rely on a diagnoser. However, the construction of a diagnoser requires the generation of the whole system space, thereby making the approach impractical even for DESs of moderate size. To avoid total knowledge compilation while preserving efficiency, a twin-engined diagnosis technique is proposed in this paper, which is inspired by the two operational modes of the human mind. If the symptom of the DES is part of the knowledge or experience of the diagnosis engine, then Engine 1 allows for efficient diagnosis. If, instead, the symptom is unknown, then Engine 2 comes into play, which is far less efficient than Engine 1. Still, the experience acquired by Engine 2 is then integrated into the symptom dictionary of the DES. This way, if the same diagnosis problem arises anew, then it will be solved by Engine 1 in linear time. The symptom dic- tionary can also be extended by specialized knowledge coming from scenarios, which are the most critical/probable behavioral patterns of the DES, which need to be diagnosed quickly

On the cost of diagnosis with disambiguation

International audienceDiagnosis consists in deciding from a partial observation of a system whether a fault has occurred. A system is diagnosable if there exists a mechanism (a diagnoser) that accurately detects faults a finite number of steps after their occurrence. In a regular setting, a diagnoser builds an estimation of possible states of the system after an observation to decide if a fault has occurred. This paper addresses diagnosability (deciding whether a system is diagnosable) and its cost for safe Petri nets. We define an energy-like cost model for Petri nets: transitions can consume or restore energy of the system. We then give a partial order representation for state estimation, and extend the cost model and the capacities of diagnosers. Diagnosers are allowed to use additional energy to refine their estimations. Diagnosability is then seen as an energy game: checking whether disambiguation mechanisms are sufficient to allow diagnosability is in 2-EXPTIME, and one can also decide whether diagnosability under budget constraint holds in 2-EXPTIME