Brief paper: Suboptimal supervisory control of Petri nets in presence of uncontrollable transitions via monitor places

Authors:
Francesco Basile;Pasquale Chiacchio;Alessandro Giua
Affiliations:
Dip. di Ing. dell'Informazione ed Ing. Elettrica, Universití di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy;Dip. di Ing. dell'Informazione ed Ing. Elettrica, Universití di Salerno, Via Ponte Don Melillo, 84084 Fisciano (SA), Italy;Dip. di Ing. Elettrica ed Elettronica, Universití di Cagliari, Piazza d'Armi, 09123 Cagliari, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

This paper deals with the problem of enforcing generalized mutual exclusion constraints (GMEC) on place/transition nets with uncontrollable transitions. An efficient control synthesis technique, which has been proposed in the literature, enforces GMEC constraints by introducing monitor places to create suitable place invariants. The method has been shown to be maximally permissive and to give a unique control structure in the case that the set of legal markings is controllable. This paper investigates on and formally shows that the class of controllers obtained by this technique may not have a supremal element for uncontrollable specifications. Moreover, it is shown that the family of monitor places enforcing an uncontrollable specification can be parameterized with respect to the solution of a linear system of equation. An algorithm to obtain such parameterization is presented here.