An Approach To Determine Controllability of Monolithic Supervisors

Abstract

In this paper we study the problem of supervisory design using Petri nets. We consider a monolithic supervisor candidate, i.e., a net obtained by concurrent composition of plant and specification, and we say that the control problem has an OR-AND GMEC solution if the set of the legal markings of such a net can be described by a disjunction/conjunctions of linear constraints. We derive some sufficient conditions, based on the boundedness of some places of the net, for the existence of such a solution.

Design of Optimal Petri Net Controllers for Disjunctive Generalized Mutual Exclusion Constraints

“…However, the solution of Moody and Antsaklis is typically suboptimal, unless each uncontrollable transition has at most one input [11]. In more general classes of systems, although there does not exist a generalized solution yet, typically an inadmissible GMEC should be transformed into a set of disjunctive admissible GMECs, or even a disjunction of conjunctive admissible GMECs [12], [13]. Furthermore, in the forbidden marking problem such as deadlock prevention problems in S 3 P R nets [14], [15], the legal marking set can also be non-convex.…”

“…By the condition in (12), it is clear that the firing of a transition t x,i 1 →i 2 ∈ T (t x ) has the same impact on the state evolution ofÑ as the firing of sequence σ = t x t i 1 i 2 inN . Theorem 5.12 ensures that if neither t x nor t i 1 i 2 is enabled butM + CN σ ≥ 0 inÑ , we can fire a mirror transition t x,i 1 →i 2 instead of firing t x and t i 1 i 2 sequentially, where σ = t x t i 1 i 2 .…”