SUPERVISORY CONTROL OF DETERMINISTIC PETRI NETS WITH REGULAR SPECIFICATION LANGUAGES

Algorithms for computing a minimally restrictive control in the contex t of supervisory control of discrete-event systems have been well deve loped when both the plant and the desired behavior are given as regula r languages. In this paper we extend such prior results by presenting an algorithm for computing a minimally restrictive control when the pl ant behavior is a deterministic Petri net language and the desired beh avior is a regular language, As part of the development of the algorit hm, we establish the following results that are of independent interes t: i) the problem of determining whether a given deterministic Petri n et language is controllable with respect to another deterministic Petr i net language is reducible to a reachability problem of Petri nets an d ii) the problem of synthesizing the minimally restrictive supervisor so that the controlled system generates the supremal controllable sub language is reducible to a forbidden marking problem, In particular, w e can directly identify the set of forbidden markings without having t o construct any reachability tree.