Compositions of (max, +) automata

Abstract

International audience<p>This paper presents a compositional modeling approach by means of (max, +) automata. The motivation is to be able to model a complex discrete event system by composing sub-models representing its elementary parts. A direct modeling of safe timed Petri nets using (max, +) automata is first introduced. Based on this result, two types of synchronous product of (max, +) automata are proposed to model safe timed Petri nets obtained by merging places and/or transitions in subnets. An asynchronous product is finally proposed to represent particular bounded timed Petri nets.</p

Supervisory control of (max,+) automata: extensions towards applications

“…A possible application to flexible manufacturing system has finally been presented as an illustration. Based on composition results from Lahaye et al (2014a), we plan to extend our results to large systems formed as synchronous products of (max,+) automata representing their subsystems. To be able to deal with state explosion problem, it would also be nice to fit our results into a heterarchical approach.…”

“…From the point of view of our control problem for DES, some recent studies have brought important advances. In fact, in the continuity of Gaubert and Mairesse (1999b), we have recently contributed to a modelling methodology for DES by means of (max,+) automata (Lahaye et al, 2014a), and identified a significant class which can be represented by deterministic (and thus unambiguous) (max,+) automata (Lahaye et al, 2014b). This class of DES that satisfies the assumptions for our control approach will be introduced in Section 5.…”

“…The approaches in Gaubert and Mairesse (1999b) and Lahaye et al (2014a) make it possible to associate a (max,+) automaton to any safe timed Petri net such that the completion date of a firing sequence in the Petri net is the same as the one of the corresponding state-transition sequence in the (max,+) automaton. This (max,+) automaton is generally non-deterministic and may have a larger language than the Petri net (i.e.…”

“…a and f ). The recent contribution (Lahaye et al, 2014a) proposes a recursive procedure which builds a deterministic (max,+) automaton equivalent to a safe timed Petri net. The equivalence corresponds to the facts that the automaton and the Petri net have the same language, and that the completion date of a firing sequence in the Petri net is the same as one of the corresponding state-transition sequence in the (max,+) automaton.…”

Initial-state detectability and initial-state opacity of unambiguous weighted automata

“…To explore the modeling power of UWAs, it is worth mentioning that the relation between max-plus automata (MPAs) and timed Petri nets (TPNs) has been investigated. From a safe TPN under the preselection policy, it is possible to derive an MPA with the same timed behaviour (Gaubert & Mairesse 1999, Lahaye et al 2015. If the race policy is considered, it has been shown that bounded TPNs can be represented by deterministic max-plus automata (DMPAs) (Komenda et al 2016, Triska & Moor 2020.…”