Compact and decentralized supervisors for general constraint enforcement in Petri net models

Abstract

This paper concerns the design of decentralized supervisors for Petri nets. In the considered framework, the set of transitions is partitioned into blocks belonging to different modules, and any local controller can operate only on the transitions of a given module. A decentralized supervisor is determined that enforces a global specification given in terms of Generalized Mutual Exclusion Constraints so that each local supervisor detects and disables transitions of a single module only. The proposed approach computes a maximally permissive solution

Decentralized monitors design for Petri net models

“…Only legal sets that are simultaneously BC-and DC-feasible result in admissible supervisors for the problem at hand. The notions of BC-and DC-feasibility extend the homologous Band D-feasibility properties introduced in (Basile et al, 2013a) to include behavioral controllability (in (Basile et al, 2013a) only the more restrictive structural controllability condition is considered). Notice in this respect that controllability cannot be ensured in the decentralization framework by analysis of the reachability graph alone, but requires additional conditions on the structure of the supervisor, thus entering in both the BCand DC-feasibility definitions.…”

“…A first extension of this problem to a decentralized setting is discussed in (Basile et al, 2013a), where multiple control sites can be employed in the design, each operating on a subset of the PN transitions. The supervisor consists of multiple local controllers, each associated to a different control site.…”

“…Specifically, (Iordache and Antsaklis, 2006) provides a sufficient condition for a set of GMECs to be enforced in a decentralized setting (denoted d-admissibility). In (Basile et al, 2013a), the focus is instead on finding a decentralized supervisor (if one exists) that preserves as many (globally) legal states as possible. The main difficulty lies in the fact that the states allowed by a decentralized supervisor do not necessarily configure a reachability subgraph compatible with all the given behavioral requirements.…”