Estimation of Least-Cost Transition Firing Sequences in Labeled Petri Nets by Using Basis Reachability Graph

Abstract

This paper develops an approach for solving the problem of least-cost transition firing sequences estimation in labeled Petri nets with unobservable transitions. Each transition in the net is labeled as either observable or unobservable, and has a nonnegative cost. Additionally, we assume that the net system is bounded, the unobservable subnet is acyclic, and the cost of each unobservable transition is strictly positive. We propose the method mainly on the basis of the notions of basis marking and basis reachability graph (BRG), which is a compact representation of the reachability graph of the net system. By sacrificing extra storage space to keep the BRG and other necessary information in memory, some time-consuming computations are moved off-line. This makes our proposed approach more feasible for on-line applications. Finally, we present a brief survey and comparison of some representative methods that use labeled Petri nets as a formalism in the literature. INDEX TERMS Basis reachability graph (BRG), discrete event system (DES), Petri net (PN), transition firing sequence.

Design of an Integrated Automation & Control System Using Petri Nets: Case Study

“…The GHENeSys model of this subsystem presents sequences of access control, activation of operating conditions, and opening of the general synoptic or mimic with access to the auxiliary windows of the SCADA (alarms, trend, reports, and statistical analyzer). Each stage is represented with macro-places and their conditions with auxiliary places and extended arcs that allow simulating its execution in any normal or dangerous situation, which is not allowed to be studied integrally in other discrete methodologies (Aly & Kotb, 2018;Borges & Lima, 2018;Lin et al, 2016;Lutz-Ley & Lopez-Mellado, 2018;Yue et al, 2019;). These macro-places encapsulate the execution details of each one, as in the case of the synoptic or general mimic which these internal details are enlarged in the low hierarchical model (Figure 7).…”

“…In (Luo et al, 2018), an approach in ordinary Petri nets is used to analyze, simulate, and verify programs in ladder diagram (LD), managing to detect unwanted sequences and finding the correct sequence using reachability graphs (RG). In (Yue et al, 2019), an analysis method is proposed using basic marking in compacted reachability graph (BRG), which allows solving the problem of estimation of low-cost transition sequences using LPN with unobservable transitions. These examples show that the design, verification, and validation in PN are not fully resolved because it is a current topic with complex methods (colored PN, RG, BRG), and they do not have full IEC61131 compatibility with integrality between hierarchical levels.…”

Diagnose de falhas para uma classe de Redes de Petri

“…Em Cabasino et al (2010) também é proposto um grafo determinístico, chamado de Grafo de Alcançabilidade Base (GAB), para, principalmente, realizar a maior parte dos cálculos offline. Entretanto, na análise de pior caso, de acordo com Yue et al (2019), o número de nós do GAB é igual ao número de marcações alcançáveis da rede. Assim, calcular o GAB tem a mesma complexidade computacional de calcular o grafo de alcançabilidade da RPR no pior caso.…”