Structural analysis and sequential resolution for estimation of guaranteed horizons in partially observable Petri nets

We introduce a semi-decidable procedure which, given a Petri net structure and a set /spl Tscr/ of transitions, synthesizes a supervisor enforcing the transitions in /spl Tscr/ to be live. We call this liveness property /spl Tscr/-liveness. When /spl Tscr/ equals the total set of Petri net transitions, /spl Tscr/-liveness corresponds to liveness. Enforcing only a subset of transitions to be live is useful when some Petri net transitions model undesired events such as failures, and/or when the Petri net structure does not allow enforcing all transitions to be live. The supervisors generated by our procedure are often least restrictive, and their synthesis is independent of the initial marking. No assumptions are made on the Petri net structure: the Petri nets may be unbounded and have integer weights. We have extended the procedure to Petri nets having uncontrollable and unobservable transitions, however, in this paper we restrict our attention to fully controllable and observable Petri nets.

We introduce a semi-decidable procedure which, given a Petri net structure and a set /spl Tscr/ of transitions, synthesizes a supervisor enforcing the transitions in /spl Tscr/ to be live. We call this liveness property /spl Tscr/-liveness. When /spl Tscr/ equals the total set of Petri net transitions, /spl Tscr/-liveness corresponds to liveness. Enforcing only a subset of transitions to be live is useful when some Petri net transitions model undesired events such as failures, and/or when the Petri net structure does not allow enforcing all transitions to be live. The supervisors generated by our procedure are often least restrictive, and their synthesis is independent of the initial marking. No assumptions are made on the Petri net structure: the Petri nets may be unbounded and have integer weights. We have extended the procedure to Petri nets having uncontrollable and unobservable transitions, however, in this paper we restrict our attention to fully controllable and observable Petri nets.

Considers the problem of enforcing linear constraints containing marking terms, firing vector terms, and Parikh vector terms. Such constraints increase the expressivity power of the linear marking constraints. We show how this new type of constraints can be enforced in Petri nets. In the case of fully controllable and observable Petri nets, we give the construction of a supervisor enforcing such constraints. In the case of Petri nets with uncontrollable and/or unobservable transitions, we reduce the supervisor synthesis problem to enforcing linear marking constraints on a transformed Petri net.

In this paper, we study fault diagnosis in discrete event systems modeled by partially observed Petri nets, i.e., Petri nets equipped with sensors that allow observation of the number of tokens in some of the places and/or partial observation of the firing of some of the transitions. We assume that the Petri net model is accompanied by a (possibly implicit) description of the likelihood of each firing sequence. Faults are modeled as unobservable transitions and are divided into different types. Given an ordered sequence of observations from place and transition sensors, our goal is to calculate the belief (namely, the degree of confidence) regarding the occurrence of faults belonging to each type. To handle information from transition and place sensors in a unified manner, we transform a given partially observed Petri net into an equivalent (as far as state estimation and fault diagnosis is concerned) labeled Petri net (i.e., a Petri net with only transition sensors), and construct a translator that translates the sensing information from place and transition sensors into a sequence of labels in the equivalent labeled Petri net. Once this transformation is established, we focus on the computation of beliefs on faults in a given labeled Petri net and construct an online monitor that recursively produces these beliefs by tracking the existence of faulty transitions in execution paths that match the sequence of labels observed so far. Using the transformed labeled Petri net and the translated observation sequence, we can then compute the belief for each fault type in partially observed Petri nets in the same way as in labeled Petri nets.

MSD-CDRL:A Generic Fusion Detection Framework for Logic Covert Attack Towards Cyber-Physical System Security

Petri 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 problem: we show how the basis coverability graph can be used to get an efficient algorithm.

In this paper, we present a fault diagnosis approach for a class of partially observed Petri nets using its structure information. With a novel graph named Diagnosis Marking Path Graph (DMPG), the proposed method does not need traverse all states of the discrete event system. For the considered Petri net, some of its transitions are unobservable including all the transitions representing faulty behaviors. In particular, a concept of diagnosis node is firstly defined. Then three diagnosis states of faults are presented based on the analysis of a DMPG, which is computed depending on the structure information of Petri nets. Finally, the validity of the method is illustrated using an example.

Linear Algebraic Design of Supervisors for Partially Observed Petri Nets

Fault-prognosability, [formula omitted]-step prognosis and [formula omitted]-step predictive diagnosis in partially observed petri nets by means of algebraic techniques

This paper studies optimal sensor selection in discrete event systems modeled by partially observed Petri nets. The goal is to place a minimum number of sensors while maintaining structural observability, i.e., the ability to uniquely determine the system state at any given time step based on sensor information up to that time step, knowledge of the system model, and an arbitrary but known initial state. The problem is important because the majority of existing control schemes for Petri nets rely on complete knowledge of the system state at any given time step. To simplify the problem, we consider two subproblems: the optimal place sensor selection (OPSS) problem and the optimal transition sensor selection (OTSS) problem. The OPSS problem is shown to be computationally hard by establishing that the corresponding decision problem is NP -complete. For this reason, we first reduce the problem to the linear integer programming problem, which can be solved optimally using existing linear integer programming solvers (at least for small problem instances), and then propose two heuristic algorithms to approximate its solution with polynomial complexity. Simulations suggest that the two proposed heuristics run faster and can find reasonably good solutions when compared to optimal methods that are based on linear integer programming solvers. Unlike the OPSS problem, the OTSS problem is solvable with polynomial complexity.

ABSTRACTIn this paper, we design a diagnostic technique for a partially observed labelled Petri net where the faults of the system are modelled by unobservable transitions. The fault detection and isolation uses an on-line count vector estimation associated with the firing of unobservable transitions exploiting the observation of firing occurrences of some observable transitions. The support of the approach is an algebraic description of the process under the form of a polyhedron developed on a receding horizon. We show that a diagnostic can be made despite that different transitions can share the same label and that the unobservable part of the Petri net can contain circuits.

This paper deals with fault diagnosis in discrete event systems modeled with partially observed Petri nets. The approach herein presented removes unnecessary information from the incidence matrix by building a reduced observable projection net using the observable complement subspace of the original net. Using this observable projection net and an off-line algorithm, a structural characterization of the diagnosability of Petri nets is proposed. The reduced observable projection net is also used to design a fault diagnoser. An illustrative example is presented to show the effectiveness of the results.

Depth-first Search Approach for Language-based Opacity Verification Using Petri Nets

This paper studies the supervisory control problem in Petri nets with unobservable transitions and uncontrollable transitions. Given a Petri net of such a type, a supervisor is designed based on the basis reachability graph in which the set of explicit transitions is a superset of the set of observable transitions. A sensor reduction method is proposed to find a minimal set of observable transitions without compromising the permissiveness. Removal of redundant observable transitions leads to a more compact control structure and a lower cost related to sensor deployment.

Current-state opacity modelling and verification in partially observed Petri nets