State Estimation of ?-free Labeled Petri Nets with Contact-Free Nondeterministic Transitions*

Abstract

In this paper we deal with the problem of estimating the marking of a labeled Petri net with nondeterministic transitions. In particular, we consider the case in which nondeterminism is due to the presence of transitions that share the same label and that can be simultaneously enabled. Under the assumption that: the structure of the net is known, the initial marking is known, the transition labels can be observed, the nondeterministic transitions are contact-free, we present a technique for characterizing the set of markings that are consistent with the actual observation. More precisely, we show that the set of markings consistent with an observed word can be represented by a linear system with a fixed structure that does not depend on the length of the observed word.

State estimation and control of nondeterministic λ-free labeled petri nets

“…We first presented a marking estimation procedure that can be applied to λ-free labeled Petri nets (the formal proof of the correctness of this procedure can be found in [6]). In particular, under the assumption that all nondeterministic transitions are contact-free, the set of markings consistent with an observed word can be described by a constraint set of linear inequalities that has a fixed structure that does not change as the length of the observed sequence increases.…”

“…In [6] we provided a systematic and efficient procedure to estimate the set of markings that are consistent with an observed word under the following assumptions:…”

“…In [6] we have shown that, under the assumptions (A1) to (A4), a fixed number of constraints, not depending on the length of the observed word w, may be used to describe the set of w-consistent markings.…”

“…In this paper we present a slightly modified version of this algorithm (see Algorithm 6) for which a formal proof has been obtained: the complete proof is not reported here for lack of space but can be found in [6].…”

Distributed Diagnosis of Place-Bordered Petri Nets

“…Petri net models have been employed to solve problems of state observability, system monitoring, alarm analysis, and fault diagnosis in several works, including [5], [6], [7], [8], [9], [10], [11]. However, to the best of our knowledge, our DDC-2 and DDC-M algorithms are the first to explore the extension of the Diagnoser Approach of [2] to modular discrete-event systems modeled by Petri nets.…”