Fault detection for discrete event systems using Petri nets with unobservable 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

Fault detection for discrete event systems using Petri nets with unobservable 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

A survey on efficient diagnosability tests for automata and bounded Petri nets

This paper presents a survey and evaluation of the efficiency of polynomial diagnosability algorithms for systems modeled by Petri nets and automata. A modified verification algorithm that reduces the state space by exploiting symmetry and abstracting unobservable transitions is also proposed. We show the importance of minimal explanations on the performance of diagnosability verifiers. Different verifiers are compared in terms of state space and elapsed time. It is shown that the minimal explanation notion involved in the modified basis reachability graph, a graph presented by Cabasino et al. [3] for diagnosability analysis of Petri nets, has great impact also on automata-based diagnosability methods. The evaluation often shows improved computation times of a factor 1000 or more when the concept of minimal explanation is included in the computation

Basis marking representation of Petri net reachability spaces and its application to the reachability problem

In this paper a compact representation of the reachability graph of a Petri net is proposed. The transition set of a Petri net is partitioned into the subsets of explicit and implicit transitions, in such a way that the subnet induced by implicit transitions does not contain directed cycles. The firing of implicit transitions can be abstracted so that the reachability set of the net can be completely characterized by a subset of reachable markings called basis makings. We show that to determine a max-cardinality-T_I basis partition is an NPhard problem, but a max-set-T_I basis partition can be determined in polynomial time. The generalized version of the marking reachability problem in a Petri net can be solved by a practically efficient algorithm based on the basis reachability graph. Finally this approach is further extended to unbounded nets

Non-Blockingness Verification of Bounded Petri Nets Using Basis Reachability Graphs -- An Extended Version With Benchmarks

In this paper, we study the problem of non-blockingness verification by tapping into the basis reachability graph (BRG). Non-blockingness is a property that ensures that all pre-specified tasks can be completed, which is a mandatory requirement during the system design stage. In this paper we develop a condition of transition partition of a given net such that the corresponding conflict-increase BRG contains sufficient information on verifying non-blockingness of its corresponding Petri net. Thanks to the compactness of the BRG, our approach possesses practical efficiency since the exhaustive enumeration of the state space can be avoided. In particular, our method does not require that the net is deadlock-free.Comment: This article is an extended version of the paper "C. Gu, Z. Ma, Z. Li and A. Giua. Non-blockingness verification of bounded Petri nets using basis reachability graphs. IEEE Control Systems Letters, doi:10.1109/LCSYS.2021.3087937, 2021" with benchmark

Distributed motion misbehavior detection in teams of heterogeneous aerial robots

This paper addresses the problem of detecting possible misbehavior in a group of autonomous mobile robots, which coexist in a shared environment and interact with each other and coordinate according to a set of common interaction rules. Such rules specify what actions each robot is allowed to perform in order to interact with the other members of the group. The rules are distributed, i.e., they can be evaluated only starting from the knowledge of the individual robot and the information the robot gathers from neighboring robots. We consider misbehaving those robots which, because of either spontaneous failures or malicious tampering, do not follow the rules and whose behavior thus deviates from the nominal assigned one. The main contribution of the paper is to provide a methodology to detect such misbehavior by observing the congruence of actual behavior with the assigned rules as applied to the actual state of the system. The presented methodology is based on a consensus protocol on the events observed by robots. The methodology is fully distributed in the sense that it can be performed by individual robots based only on the local available information, it has been theoretically proven and validated with experiments involving real aerial heterogeneous robots

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a 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 constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an 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 the construction of the reachability graph and has wide applicability.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl