Feedback Control Logic for Backward Conflict Free Choice Nets

Abstract

This paper discusses the forbidden state problem, as specified by generalized mutual exclusion constraints, in the context of supervisory control of discrete event systems modelled by Petri nets. The case of backward-conflict-free and free-choice uncontrollable subnets is considered and it is shown how to transform such subnets in well-formed free-choice nets. Then, the wellformed free-choice nets are decomposed in marked graph components by recurring to minimal T-invariants. The forbidden state problem is so reformulated for the obtained marked graph components into an equivalent one which is shown to be a linear programming problem. Thus, improving existing results in literature, a polynomial complexity solution, suitable for on-line control, is achieved. Free-choice relationship and cycle modelling, that frequently occur in real-life situations, are so allowed in the uncontrollable subnet.Index Terms-Backward conflict free net, free choice net, Petri nets, state feedback, supervisory control.

Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

“…In many supervisory control problems in Petri nets, the legal marking set can be written as a finite union of integer convex sets 1 In such a case the legal marking set can always be written as an OR-AND GMEC W and can then be enforced by a place/transition controller that is maximally permissive if W is bounded [22].…”

“…end for 11: end if In the first loop, f 1 is treated and c 1 = 3 remainder places q 0 1 , q 1 1 , and q 2 1 are added toP. The remainder place q 1 1 is marked with one token since a…”

“…Since the monitor design does not require to enumerate the reachability set but is only based on the net structure, the state explosion problem could be avoided and the controller design process is quite efficient. GMECs are an example of Petri net structural approaches that have been proved to be useful in a wide range of contexts [25,1,31,30,2,26,4,27,22,24].…”

An Efficient Approach for Online Diagnosis of Discrete Event Systems

“…is totally unimodular. Moreover, if the subnet is a Backward-Conflict Free-Choice Net 5 , then it can be decomposed in marked graph components and, even in this case, the solution can be obtained as solutions of linear programming problems [19].…”

An Approach To Determine Controllability of Monolithic Supervisors

“…They extends the class of control problems that can be solved by automata and provide many efficient and well founded approaches for supervisory control (Holloway et al, 1997). In particular several interesting results, have been obtained when the desired behavior of the plant is described by state specification: in this case efficient algorithms exists to compute a controller even in the presence of uncontrollable transition: we recall in this context the work of Giua et al (1992); Moody and Antsaklis (2000); Holloway et al (2004); Basile et al (2007); Luo and Nonami (2011); Uzam (2010); Iordache et al (2013) In comparison, relatively few works have discussed how Petri net models may be used to design supervisors for language specifications. We consider the monolithic supervisory design that requires: (a) to construct a monolithic supervisor candidate (MSC) by the concurrent composition of the plant with the specification, to check this structure for controllability and nonblockingness, and eventually to refine it.…”