A strategy for estimation in timed Petri nets

International Journal of Systems Science: Operations & Logi

Khedher

et al. 2018

Self Cite

In this paper, we design a diagnostic technique for a partially observed labeled Petri net where the faults of the system are modeled 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.

Section: Resultsmentioning

confidence: 99%

Diagnostic based on estimation using linear programming for partially observable petri nets with indistinguishable events

Chouchane

International Journal of Systems Science: Operations & Logi

Khedher

et al. 2018

Self Cite

“…In this paper, the aim is to treat P-time PNs by a simplification under the form of a P-timed PN while the paper [11] considers P-timed PNs by building an untimed PN and analyzing the candidate count vectors. The objective of [12] is also different as this study focuses on the estimation of sequences in untimed PNs.…”

Section: Strategy and Contextmentioning

confidence: 99%

Two-staged approach for estimation of sequences in partially observable P-time Petri nets on a sliding horizon with schedulability analysis

International Journal of Control

Bonhomme

2023

In this paper, we consider the on-line estimation of current subsequences for Partially Observable P-time Petri Nets and their starting markings on a sliding horizon composed of steps defined by two successive occurrences of observable transition firings. We propose a general strategy composed of two phases: Phase 1 exploits a simplification of the P-time Petri net under the form of a Timed Petri net; considering a candidate count vector and the relevant starting marking proposed at Phase 1, Phase 2 makes a schedulability analysis by building a system of relations which can be represented by an acyclic conflict-free computation graph. The complete approach avoids the generation of sets which is generally time and space consuming, and provides an optimal solution for each subproblem by using efficient standard tools.

“…Consider the Petri net of Fig. 2 and the relevant untimed system (12). We take M <1> = 1 0 and the observation is y 2 at step < 1 >: so, y <1>…”

Section: Guaranteed Time Horizon For Step < 1 >mentioning

confidence: 99%

“…The paper [1] focused on the same aim by applying the Fourier-Motzkin algorithm in partially observable Petri nets in the field of fault detection. While the objective of the paper [12] is a schedulability analysis of sequences relevant to candidate count vectors, this proposed paper follows another strategy as its aim is to directly provide sequences without searching candidate count vectors and to estimate a current majorant of the necessary horizon on-line.…”

Section: Introductionmentioning

confidence: 99%

Counter approach for the estimation of optimal sequences in Partially Observable Untimed Petri Nets

Discrete Event Dyn Syst

2021

In this paper, we consider the on-line estimation of optimal current subsequences in Partially Observable Untimed Petri Nets. Applying the counter approach classically used in max-plus algebra for Timed Petri nets, the idea is to exploit the assumption of a non immediate consumption of the tokens for each place which introduces an order of precedence between events. The approach can estimate a global price depending on the costs and gains provided by the tasks. The estimation of optimal sequences is based on the determination of a time horizon necessary to describe the sequences. The estimation is relevant to a step defined by two successive occurrences of observable transition firings. We show that the approach can consider any optimization problem if the dates of the observations are known or, if a guaranteed horizon can be computed which is always possible when the unobservable subnet satisfies a weak assumption close to the structural boundedness (relaxed structurally boundedness). As the technique avoids the generation of sets, the approach does not depend on their cardinalities and is numerically efficient.