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

Abstract

In this paper, supervisory control of (max,+) automata is studied. The synthesis of maximally permissive and just-in-time supervisor, as well as the synthesis of minimally permissive and just-after-time supervisor, are proposed. Results are also specialised to non-decreasing solutions, because only such supervisors can be realised in practice. The inherent issue of rationality raised recently is discussed. An illustration of concepts and results is presented through an example of a flexible manufacturing system.

Keywords:

• discrete event systems
• logical and timed behaviours
• (max,+) automata
• supervisory control

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Petri nets are very well known for the modelling of DES (see, for example, Murata, 1989; David & Alla, 2010, for an introduction).

2. This definition is slightly different from that in Gaubert (1995) where initial and final delays are considered. Note that there is no loss of generality here since an automaton with initial and final delays can always be transformed into an equivalent automaton without such delays by adding new states and by considering these delays as state-transition durations associated to new fictive initial and final events.

3. Notation G_s(a) is rough because G_s is not specified as a map defined on alphabet A.

4. Please note that the complexity of this procedure remains to be shown.

5. ?http://www.cmap.polytechnique.fr/ gaubert/MaxplusToolbox.html?

6. ?https://www.lrde.epita.fr/wiki/Vcsn?

7. ?http://www.openfst.org?